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Quantum simulation
Open accessAbstract
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.
Overview
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TL;DR
This review surveys quantum simulation—using controllable quantum systems to emulate less accessible quantum systems—covering digital and analog approaches, physical platforms, resource requirements, and applications. It argues that practical quantum simulators may be realized before full-scale quantum computers, with neutral atoms in optical lattices and trapped ions currently among the most advanced platforms.
Key findings
- Classical simulation of quantum systems scales exponentially: representing the state of 40 spin-1/2 particles requires \(2^{40} \approx 10^{12}\) numbers, about \(3.2 \times 10^{13}\) bits or 4 TB in single precision, while 80 spins would require about \(3.8 \times 10^{25}\) bits.
- Quantum simulators can store this information more compactly: the state of 40 spin-1/2 particles that needs a 4 TB classical register can be represented by a 40-qubit register.
- Resource estimates for digital quantum simulation (DQS) of chemical dynamics suggest that outperforming current classical computers would require at least 100 qubits and over 200,000 quantum gates per step; for molecular hydrogen, a precision of \(\pm 10^{-4} E_h\) was achieved with about 522 gates.
- Experimentally, the most advanced DQS has been realized with trapped ions, simulating spin models with up to six spins and one experiment requiring sequences of more than 100 quantum gates; neutral atoms in optical lattices are described as the most advanced platform for analog quantum simulation (AQS), with hundreds of ions used in a two-dimensional ion array for a spin-system simulation.
Methods
- This is a review article, not a primary experimental or theoretical study; it synthesizes theoretical and experimental literature on quantum simulation.
- It organizes the field into digital quantum simulation, analog quantum simulation, and quantum-information-inspired classical algorithms, and discusses resource estimation, fault tolerance, physical realizations, and applications.
- The paper reviews platforms including neutral atoms, trapped ions, polar molecules, nuclear and electronic spins, superconducting circuits, photons, and other systems, with applications in condensed-matter physics, high-energy physics, cosmology, atomic physics, quantum chemistry, open quantum systems, nuclear physics, and interferometry.
Limitations
- The paper states that given the breadth of topics, not all technical details can be provided and directs readers to references; it also notes that initial-state preparation and measurement in AQS have not been thoroughly discussed in the literature.
- The paper states that resource estimation for AQS has not received much work, and that decoherence and errors in quantum simulation require further study, especially for each physical implementation.
- Evident from the text: as a broad review, it does not present a systematic meta-analysis or new primary data, and its performance comparisons rely on cited proposals and experiments rather than a unified benchmark.
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120 Not checked yet · 60 No basis given · 55 Own interpretation
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In the paper
“In fact, some proofof-principle experiments on quantum simulation have already been realized (see e.g. (Friedenauer et al. , 2008; Gerritsma et al. , 2010; Greiner et al. , 2002; Kim et al. , 2010; Lanyon et al. , 2010; Leibfried et al. , 2002; Neeley et al. , 2009)).”
What the sources say
- Not checked yetcites Friedenauer et al., 2008
- Not checked yetcites Gerritsma et al., 2010
- Not checked yetcites Greiner et al., 2002
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“This implies storing 2 40 ≈ 10 12 numbers for | φ 〉”
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“For example, the storage capacity of N qubits is exponentially larger than that of N classical bits .”
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“Double the number of spins, and ∼ 3 . 8 × 10 25 bits (or 5 × 10 12 TB) would be required.”
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“Calculating the time evolution of this system requires exponentiating a 2 N × 2 N matrix.”
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“For instance, representing the state of N spin-1/2 particles requires 2 N numbers (namely the complex probability amplitudes for the different spin configurations), and this is without including the particles' motional degrees of freedom.”
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“Assuming single precision, about ∼ 3 . 2 × 10 13 bits, that is 4 TB (terabytes), are required to represent the spin state of 40 particles in a computer memory.”
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“Going back to the example given in the previous section, the quantum state of N = 40 spin-1/2 particles, which would require a 4TB classical memory register, can be represented by a 40qubit (i.e. 5-quantum-byte) register.”
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“Furthermore high-fidelity one-, two and three-qubit quantum gates have been demonstrated.”
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“In quantum magnets, the transition from a para- to an anti-ferromagnet was emulated using two trapped calcium ions in (Friedenauer et al. , 2008).”
What the sources say
- Not checked yetcites Friedenauer et al. , 2008
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“In a recent experiment, the motional degrees of freedom of atoms trapped in an optical lattice were used to simulate ferromagnetic, antiferromagnetic and frustrated classical spin configurations (Struck et al. , 2011).”
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- Not checked yetcites Struck et al. , 2011
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“Recently, it was shown that the propagation of photons in a network of beam splitters is in general a computationally difficult task for classical computers even for a few tens of photons (Aaronson and Arkhipov, 2011), and corresponding experiments with up to four photons were performed (Broome et al. , 2013; Crespi et al. , 2013; Spring et al. , 2013; Tillmann et al. , 2013).”
What the sources say
- Not checked yetcites Aaronson and Arkhipov, 2011
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“Individual control and measurement have been demonstrated (Mariantoni et al. , 2011).”
What the sources say
- Not checked yetcites Mariantoni et al. , 2011
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“Since no error correction was used, the fidelity of the DQS implementation was somewhat lower than for the AQS implementation in the same system (see (Friedenauer et al. , 2008)).”
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- Not checked yetcites Friedenauer et al. , 2008
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“With the current experimental state-of-the-art techniques, the most advanced DQS has been realized with trapped ions (Lanyon et al. , 2011).”
What the sources say
- Not checked yetcites Lanyon et al. , 2011
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“even with a small-scale quantum simulator exciting physical phenomena could be explored”
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“A proposed solution to this problem came in the new type of computer envisaged by Richard Feynman (Feynman, 1982) - the quantum computer.”
What the sources say
- Not checked yetcites Feynman, 1982
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In the paper
“Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems.”
- Also stated in: § I. INTRODUCTION · p. 2 · boosted
“Thirty years ago, in the early 1980s, it had become clear that simulating quantum mechanics is a very challenging problem (Feynman, 1982; Manin, 1980).”
What the sources say
- Not checked yetcites Feynman, 1982
- Not checked yetcites Manin, 1980
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“Furthermore, simulating the temporal evolution of the system requires a number of operations that also increases exponentially with the size of the system.”
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“One obvious difficulty is the huge amount of computer memory needed to store the quantum state of a large physical system.”
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“Second, the technologies required for the coherent control of quantum systems have matured enough to allow for the physical implementation of practical quantum simulation in the very near future.”
What the sources say
- Not checked yetcites Buluta et al., 2011
- Not checked yetcites Ladd et al., 2010
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“More than a decade later, it was shown (Lloyd, 1996) that a quantum computer (i.e., an ensemble of welldefined qubits that can be initialized, measured and on which universal quantum gates can be performed) can indeed act as a universal quantum simulator.”
What the sources say
- Not checked yetcites Lloyd, 1996
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“This state is described by a number of parameters that grows exponentially with the system size (which is generally defined as the number of particles or degrees of freedom in the system).”
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“Therefore, the simulation of quantum systems in general remains a hard task even for today's supercomputers.”
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“It is therefore expected that practical quantum simulation will become a reality well before full-fledged quantum computers.”
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“This exponential explosion is unavoidable, unless approximation methods (e.g. Monte Carlo methods) are used.”
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“However, a quantum computer (as defined above) is not necessarily required for implementing quantum simulation.”
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“Furthermore, it must be stressed that the implemented unitary operation (i.e. that obtained from the decomposition into single- and two-qubit gates) is generally an approximation of the desired unitary evolution.”
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In the paper
“As a result, when taken as a whole, the decomposition of U cannot be obtained efficiently using classical methods.”
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In the paper
“Note that finding an efficient decomposition in terms of universal gates can in itself be a difficult problem (Daskin and Kais, 2011).”
What the sources say
- Not checked yetcites Daskin and Kais, 2011
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In the paper
“Other methods of solving quantum many-body problems such as density functional theory, mean-field theories, many-body perturbation theories or Green's function-based methods, coupled clusters, etc., (see (Fetter and Walecka, 2003; Thouless, 1972; Zagoskin, 1998)) have similar validity criteria that restrict their applicability to well-behaved systems.”
What the sources say
- Not checked yetcites Fetter and Walecka, 2003
- Not checked yetcites Thouless, 1972
- Not checked yetcites Zagoskin, 1998 source
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“In (Wang et al. , 2011) a state-preparation algorithm that incorporates quantum simulation was proposed: the time evolution of the quantum system is simulated including the interaction with ancilla, i.e. auxiliary, qubits that can inject or absorb any specified amount of energy from the system, thus preparing any desired energy eigenstate.”
What the sources say
- Not checked yetcites Wang et al., 2011
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“The importance of measurement must be stressed because the success of quantum simulation ultimately depends on the ability to extract useful information from the simulator.”
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“A quantum algorithm for preparing a pure state of a molecular system with a given number m of electrons occupying a given number n of spin orbitals that exhibits polynomial scaling in m (regardless of n ) was proposed in (Wang et al. , 2009) (see Figure 2).”
What the sources say
- Not checked yetcites Wang et al., 2009
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In the paper
“while in (Kassal et al. , 2008) it was shown that most commonly used chemical wave functions can be efficiently prepared.”
What the sources say
- Not checked yetcites Kassal et al., 2008
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In the paper
“However, QST requires resources that grow exponentially with the size of the system, making it inefficient for large quantum systems.”
What the sources say
- Not checked yetcites D'Ariano et al., 2003
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In the paper
“The advantage of quantum simulators over classical devices is that, being quantum systems themselves, they are capable of storing large amounts of information in a relatively small amount of physical space.”
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“Such stochastic methods generally work well when the functions being integrated do not change sign (and ideally vary slowly with respect to the relevant variables), such that sampling the function at a relatively small number of points gives a good approximation to the integral of the function.”
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“For example, a method for generating a state that encodes the antisymmetrized many-particle state of fermions (including all the possible permutations), starting from an unsymmetrized state (e.g. | 000 · · · 0 〉 ), with polynomial resources was given in (Abrams and Lloyd, 1997).”
What the sources say
- Not checked yetcites Abrams and Lloyd, 1997
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In the paper
“Nevertheless, it is possible to efficiently simulate any finitedimensional local Hamiltonian.”
What the sources say
- Not checked yetcites Lloyd, 1996
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- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“These methods allow the evaluation of phase space integrals for many-body problems in a time that scales polynomially with the number of particles.”
What the sources say
- Not checked yetcites Suzuki, 1993
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In the paper
“If [ H l , H l ′ ] = 0 for all l and l ′ , then”
- Also stated in: § A. Digital quantum simulation (DQS) · p. 5 · plain
“In this case, the decomposition of U into a sequence of local gates is straightforward.”
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- Also stated in: § A. Digital quantum simulation (DQS) · p. 5 · plain
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In the paper
“The drawback of this approach is that high accuracy comes at the cost of very small ∆ t and therefore a very large number of quantum gates.”
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“This is particularly important since all local spin systems, and all Hamiltonians that can be efficiently mapped to such systems, are included in this class.”
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In the paper
“If the time evolution of the simulator reproduces the time evolution of the simulated system, the desired final state can be obtained without the need for numerically exponentiating a 2 N × 2 N matrix.”
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“For some quantum systems, especially fermionic and frustrated systems, the numerical evaluation of the integrals encounters the problem of sampling with non-positive-semidefinite weight functions, which is the so-called sign problem [see, e.g. (Troyer and Wiese, 2005)].”
What the sources say
- Not checked yetcites Troyer and Wiese, 2005
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In the paper
“Although the example above might look simple, the efficient simulation of a general many-body interaction Hamiltonian using two-body interactions is by no means easy (Bennett et al. , 2002; Nielsen et al. , 2002).”
What the sources say
- Not checked yetcites Bennett et al., 2002
- Not checked yetcites Nielsen et al., 2002
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- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“Fortunately, for particular cases of interest efficient state preparation is possible.”
What the sources say
- Not checked yetcites Abrams and Lloyd, 1997
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- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“However, from the graph in Figure 6, it follows that in order to outperform current classical computers at least 100 qubits and over 200,000 quantum gates per step would be required.”
What the sources say
- Not checked yetcites Kassal et al. , 2008
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In the paper
“In (Tseng et al. , 2000) it was demonstrated, through calculations and a nuclear magnetic resonance (NMR) experiment, that in the quantum simulation of open systems it is possible to exploit the natural decoherence of the simulator by varying the choice of mapping between the”
What the sources say
- Not checked yetcites Tseng et al. , 2000
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In the paper
“The interaction between the system and the environment could be qualitatively different from that between the simulator and its environment (Brown, 2007).”
What the sources say
- Not checked yetcites Brown, 2007
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In the paper
“With this analogy, effects such as Zitterbewegung and the Klein paradox can be studied in a non-relativistic quantum system (Gerritsma et al. , 2010, 2011).”
What the sources say
- Not checked yetcites Gerritsma et al. , 2010, 2011
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In the paper
“In this sense, AQS has the additional advantage that physical quantities can be measured directly, without the need for computational manipulation of measurement results as in DQS.”
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In the paper
“This gives a total of n (3 N -6) + 4 m qubits.”
What the sources say
- Not checked yetcites Kassal et al. , 2008
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In the paper
“In an interesting recent development, classical numerical algorithms for the simulation of quantum many-body systems came out of research on quantum information theory (For detailed studies on the subject, see e.g. (Verstraete and Cirac, 2004; Verstraete et al. , 2004; Vidal, 2008)).”
What the sources say
- Not checked yetcites Verstraete and Cirac, 2004
- Not checked yetcites Verstraete et al. , 2004
- Not checked yetcites Vidal, 2008
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In the paper
“With the identifications c ≡ 2 η ˆ ω ∆ and mc 2 ≡ ℏ Ω, H I has the same form as H D .”
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In the paper
“An important advantage of AQS is that it could be useful even in the presence of errors, up to a certain tolerance level.”
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In the paper
“The second example of a mapping between a quantum system and its simulator is the trapped-ion simulation of the Dirac equation (Gerritsma et al. , 2010; Lamata et al. , 2007).”
What the sources say
- Not checked yetcites Gerritsma et al. , 2010
- Not checked yetcites Lamata et al. , 2007
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In the paper
“The authors found that the computation time grows exponentially with desired precision.”
What the sources say
- Not checked yetcites Clark et al. , 2009a
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In the paper
“Using a quantum simulator instead of a classical computer does not necessarily provide an efficient solution to the problem of simulating quantum systems.”
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In the paper
“A simple argument could go as follows: if the noise level that is naturally present in the simulator is lower than the noise level in the simulated system, then it is rather straightforward to artificially supplement noise in the simulator so that the combined noise in the simulator faithfully mimics that present in the simulated system.”
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In the paper
“Indeed, it was pointed out in (Brown et al. , 2006) that several current algorithms for quantum simulation exhibit poor scaling as a function of desired accuracy, even if they seem efficient based on the scaling with system size.”
What the sources say
- Not checked yetcites Brown et al. , 2006
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In the paper
“A precision of ± 10 -4 E h , where E h ≈ 27 . 21 eV, is achieved for about 522 gates.”
What the sources say
- Not checked yetcites Lanyon et al. , 2010
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In the paper
“Using matrix product states (MPS) and projected entangled-pair states (PEPS) one can simulate more efficiently infinitesize quantum lattice systems in one and two dimensions.”
What the sources say
- Not checked yetcites Verstraete and Cirac, 2004
- Not checked yetcites Verstraete et al. , 2004
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In the paper
“However, in other situations one must rewrite H sim in order to obtain the mapping H sys ↔ H sim .”
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In the paper
“Neutral atoms in optical lattices are very well suited for mimicking solid-state systems.”
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In the paper
“Arrays of quantum dots could be realized using twodimensional mesh gates (Byrnes et al. , 2008; Manousakis, 2002) (see Figure 13).”
What the sources say
- Not checked yetcites Byrnes et al. , 2008
- Not checked yetcites Manousakis, 2002
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In the paper
“The high-fidelity one-, two-, and even three-qubit (Toffoli) gates implemented with trapped ions have resulted in the most advanced implementations of DQS to date (Barreiro et al. , 2011; Lanyon et al. , 2011).”
What the sources say
- Not checked yetcites Barreiro et al. , 2011
- Not checked yetcites Lanyon et al. , 2011
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In the paper
“By tuning interatomic interactions using Feshbach resonances, it was possible to investigate the crossover from a Bardeen-Cooper-Schrieffer (BCS) state of weakly attractive fermions to a Bose-Einstein condensate (BEC) of tightly bound fermion pairs (Regal et al. , 2004; Zwierlein et al. , 2005).”
What the sources say
- Not checked yetcites Regal et al. , 2004
- Not checked yetcites Zwierlein et al. , 2005
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In the paper
“For example, when simulating spin Hamiltonians with degenerate ground states using trapped ions, spontaneous emission of the ions drives the system to states outside the Hilbert space used in the system-simulator mapping (Brown, 2007).”
What the sources say
- Not checked yetcites Brown, 2007
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In the paper
“However, a quantum system that is not a potential quantum computer could still implement AQS.”
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In the paper
“Another system that could be used for quantum simulation is electron spins in semiconductor quantum dots (Hanson and Awschalom, 2008).”
What the sources say
- Not checked yetcites Hanson and Awschalom, 2008
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In the paper
“Furthermore, quantum dots with large tunnel coupling can act as 'artificial molecules'.”
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In the paper
“Superconducting circuits (Clarke and Wilhelm, 2008; You and Nori, 2005, 2011) (see Figure 14) can also be used as quantum simulators.”
What the sources say
- Not checked yetcites Clarke and Wilhelm, 2008
- Not checked yetcites You and Nori, 2005, 2011
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In the paper
“Disorder, noise and other imperfections might affect the reliability of the quantum simulation (Hauke et al. , 2012).”
What the sources say
- Not checked yetcites Hauke et al. , 2012
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In the paper
“Note that the simulation of open quantum systems does not necessarily require the inclusion of the decoherence of the simulator (Piilo and Maniscalco, 2006; Schneider and Milburn, 2001).”
What the sources say
- Not checked yetcites Piilo and Maniscalco, 2006
- Not checked yetcites Schneider and Milburn, 2001
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In the paper
“The different transitions between pairs of energy levels generally have distinct resonance frequencies, allowing the addressing of the individual transitions based on their frequencies.”
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In the paper
“Atoms in cavity arrays (see Figure 12) (Angelakis et al. , 2007; Brandao et al. , 2007; Greentree et al. , 2006; Hartmann et al. , 2006) could also be used as quantum simulators (see also (Kimble, 2008)).”
What the sources say
- Not checked yetcites Angelakis et al. , 2007
- Not checked yetcites Brandao et al. , 2007
- Not checked yetcites Greentree et al. , 2006
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In the paper
“A quantum simulation of the Mott insulator-superfluid phase transition in the Hubbard model can be realized by adjusting the depth of the optical lattice, which mainly modifies the tunneling strength and to a lesser extent modifies the on-site interaction strength, or by controlling the on-site interactions via Feschbach resonances (Lewenstein et al. , 2007)”
What the sources say
- Not checked yetcites Lewenstein et al. , 2007
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In the paper
“Using laser-assisted tunneling and lattice tilting, (Simon et al. , 2011) achieved the simulation of an antiferromagnetically coupled spin chain in an external magnetic field.”
What the sources say
- Not checked yetcites Simon et al. , 2011
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In the paper
“A rather unconventional example of a quantum simulator is a two-component BEC in which the propagation of sound waves could simulate some aspects of cosmic inflation (Fischer and Sch¨ utzhold, 2004).”
What the sources say
- Not checked yetcites Fischer and Sch¨ utzhold, 2004
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In the paper
“The fact that superconducting circuits can be produced in large numbers and 'wired' together on a chip offers a rather straightforward way of realizing various lattice geometries.”
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In the paper
“The latter approach has been experimentally realized with linear optics (Lu et al. , 2009).”
What the sources say
- Not checked yetcites Lu et al. , 2009
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In the paper
“Spin glasses can be efficiently simulated using DQS.”
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In the paper
“a two-qubit version of the algorithm was experimentally realized using NMR (Yang et al. , 2006).”
What the sources say
- Not checked yetcites Yang et al. , 2006
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In the paper
“The advantage over real atoms is that superconducting circuits can be designed and constructed to tailor their characteristic frequencies, interaction strengths and so on.”
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In the paper
“There are also numerous similarities between the behavior of superfluid helium and cosmological phenomena, such as processes in the early universe, as discussed in detail in (Volovik, 2009).”
What the sources say
- Not checked yetcites Volovik, 2009 source
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In the paper
“Depending on the tunnel coupling strengths, electron distribution, and shell structure, the dots can form both ionicand covalent-like bonds.”
What the sources say
- Not checked yetcites Smirnov et al. , 2007
plainconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“produce Schr¨ odinger-cat states”
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In the paper
“Recently it has been demonstrated that Hawking radiation can be measured in a classical analog system, namely water surface waves (Weinfurtner et al. , 2011).”
What the sources say
- Not checked yetcites Weinfurtner et al. , 2011
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In the paper
“Superconducting circuits can also be used for new types of masers, lasers and single-photon generators (You et al. , 2007).”
What the sources say
- Not checked yetcites You et al. , 2007
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In the paper
“Superconducting circuits have also been used to engineer selection rules and thus create combinations of selection rules that are not possible with natural atoms (Deppe et al. , 2008; de Groot et al. , 2010; Harrabi et al. , 2009; Liu et al. , 2005).”
What the sources say
- Not checked yetcites Deppe et al. , 2008
- Not checked yetcites de Groot et al. , 2010
- Not checked yetcites Harrabi et al. , 2009
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In the paper
“study Landau-Zener-St¨ uckelberg interferometry (Shevchenko et al. , 2010)”
What the sources say
- Not checked yetcites Shevchenko et al. , 2010
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In the paper
“In contrast with naturally occurring atoms, artificial atoms can be lithographically designed to have specific characteristics, such as a large dipole moment or particular transition frequencies.”
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In the paper
“The Jaynes-Cummings Hamiltonian can be realized with superconducting circuits (see, e.g. (Schoelkopf and Girvin, 2008; Wallraff et al. , 2004; You and Nori, 2003, 2005, 2011; Zueco et al. , 2009)).”
What the sources say
- Not checked yetcites Schoelkopf and Girvin, 2008
- Not checked yetcites Wallraff et al. , 2004
- Not checked yetcites You and Nori, 2003, 2005, 2011
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“These circuits can provide analogues of sideband cooling and Sisyphus cooling (Grajcar et al. , 2008; Nori, 2008) (see Figure 24).”
What the sources say
- Not checked yetcites Grajcar et al. , 2008
- Not checked yetcites Nori, 2008
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“simulate the Einstein-Podolsky-Rosen experiment (You and Nori, 2005).”
What the sources say
- Not checked yetcites You and Nori, 2005
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In the paper
“There is a deep analogy between natural atoms and the artificial atoms formed, for example, by electrons in small superconducting circuits (You and Nori, 2005, 2011).”
What the sources say
- Not checked yetcites You and Nori, 2005, 2011
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“An application of DQS with a few qubits is the study of the dynamics of simple quantum maps (Georgeot, 2004; Levi and Georgeot, 2004; Schack, 1998; Terraneo et al. , 2003).”
What the sources say
- Not checked yetcites Georgeot, 2004
- Not checked yetcites Levi and Georgeot, 2004
- Not checked yetcites Schack, 1998
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Various reaction regimes and different reaction products can be obtained by varying the speed of voltage changes applied to the gates forming the quantum dots.”
What the sources say
- Not checked yetcites Smirnov et al. , 2007
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In the paper
“Moreover, they can be used to test Bell inequalities (Ansmann et al. , 2009)”
What the sources say
- Not checked yetcites Ansmann et al. , 2009
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In the paper
“The effects of those fields on the circuits are the analogues of the Stark and Zeeman effects in atoms.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The simulation of chemical dynamics is also achievable in polynomial time (Kassal et al. , 2008).”
What the sources say
- Not checked yetcites Kassal et al. , 2008
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“It has been shown that in some cases the quantum approach to the kicked Harper model can provide a polynomial gain as compared to classical algorithms.”
What the sources say
- Not checked yetcites Levi and Georgeot, 2004
plainconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“The ability to simulate various Hamiltonians could then be useful for realizing practical adiabatic quantum computation (Ashhab et al. , 2006).”
What the sources say
- Not checked yetcites Ashhab et al. , 2006
hedgedconditional- Asserted: passes — The authors put it forward as true.
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- Probably not a substantial claim. 96
- It may state two separate claims as one. 54
In the paper
“In a recent experiment, the predictions of the two-dimensional Mott-Hubbard model were tested for electrons in an artificial honeycomb lattice (Singha et al. , 2011).”
What the sources say
- Not checked yetcites Singha et al. , 2011
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“As for scalability, circuits containing 512 qubits have been fabricated (Harris, 2012; Harris et al. , 2010), although quantum coherence was not tested on these circuits in the same way that coherence is commonly tested in other experiments using small numbers of qubits.”
What the sources say
- Not checked yetcites Harris, 2012
- Not checked yetcites Harris et al. , 2010
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
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In the paper
“Recently, it was shown that the propagation of photons in a network of beam splitters is in general a computationally difficult task for classical computers even for a few tens of photons (Aaronson and Arkhipov, 2011), and corresponding experiments with up to four photons were performed (Broome et al. , 2013; Crespi et al. , 2013; Spring et al. , 2013; Tillmann et al. , 2013).”
What the sources say
- Not checked yetcites Broome et al. , 2013
- Not checked yetcites Crespi et al. , 2013
- Not checked yetcites Spring et al. , 2013
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“For example, the quantum phase transition from a superfluid to a Mott insulator phase, predicted in (Fisher et al. , 1989), was first observed in 2002 (Greiner et al. , 2002) in an ensemble of atoms trapped in an optical lattice.”
What the sources say
- Not checked yetcites Fisher et al. , 1989
- Not checked yetcites Greiner et al. , 2002
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“As discussed in Section VI.A, an AQS of the BoseHubbard model using atoms in optical lattices was proposed in (Jaksch et al. , 1998) and implemented in (Greiner et al. , 2002).”
What the sources say
- Not checked yetcites Jaksch et al. , 1998
- Not checked yetcites Greiner et al. , 2002
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“Furthermore, more than 200 superconducting resonators were recently fabricated on a single chip (Houck et al. , 2012).”
What the sources say
- Not checked yetcites Houck et al. , 2012
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Photons have been used to calculate the possible fractional statistics of anyons using a six-photon graph state (Lu et al. , 2009), to calculate the energy spectrum of the hydrogen molecule to 20 bits of precision (Lanyon et al. , 2010) and to simulate frustrated spin systems (Ma et al. , 2011).”
What the sources say
- Not checked yetcites Lu et al. , 2009
- Not checked yetcites Lanyon et al. , 2010
- Not checked yetcites Ma et al. , 2011
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“State-of-the-art superconducting qubits have coherence times exceeding 100 µ s (i.e. decoherence rates below 10 kHz), which is quite high considering that other energy scales in the circuit are typically in the range 10 MHz - 10 GHz.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
In the paper
“As for AQS, optical lattices have been used to experimentally realize a disordered system that may lead to the observation of a Bose glass phase (Fallani et al. , 2007).”
What the sources say
- Not checked yetcites Fallani et al. , 2007
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“In these experiments, simulations of various spin models with up to six spins have been demonstrated, with one experiment requiring sequences of more than 100 quantum gates.”
What the sources say
- Not checked yetcites Lanyon et al. , 2011
boosted- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“individual control and readout are difficult to realize for atoms in optical lattices”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“while for other systems that is not a problem”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“With the exception of atoms in optical lattices, quantum simulators cannot yet handle large arrays of qubits.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The machine would have the capacity to contain an exponentially large amount of information without using an exponentially large amount of physical resources, thus making it a natural tool to perform quantum simulation.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Other potential application areas include highenergy physics, quantum chemistry, cosmology and nuclear physics.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“With the latest advances in the coherent manipulation of quantum systems (Buluta et al. , 2011; Ladd et al. , 2010), such as atoms in optical lattices, trapped ions, nuclear spins, superconducting circuits, or spins in semiconductors, practical applications of quantum simulation can be expected in the coming years.”
What the sources say
- Not checked yetcites Buluta et al., 2011
- Not checked yetcites Ladd et al., 2010
plainconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, depending on the specifics of the problem under study, good approximations are not always available or they also face some limitations.”
plainconditional- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For instance, in condensedmatter physics, quantum simulation would allow the study of many difficult problems, such as quantum phase transitions, quantum magnetism or highT c superconductivity.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Simpler quantum devices that mimic the evolution of other quantum systems in an analog manner could be used for this task (note that these are not universal simulators, but rather problem-specific machines).”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Moreover, note that ancilla qubits are required, which adds to the resource requirements (see Section V. B).”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This sounds very promising, but the quantum simulation problem is not really solved unless the initial state preparation, the implementation of the time evolution and the measurement are realized using only polynomial resources.”
plainconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“This question has been thoroughly studied, and several methods have been developed (see, e.g., (Berry et al. , 2007; Bravyi et al. , 2008; Bremner et al. , 2005; Brown et al. , 2011; Dodd et al. , 2002; D¨ ur et al. , 2008; Hastings, 2006; Wang and Zanardi, 2002; Wocjan et al. , 2002a,b,c)), but it still remains a difficult problem.”
What the sources say
- Not checked yetcites Berry et al., 2007
- Not checked yetcites Bravyi et al., 2008
- Not checked yetcites Bremner et al., 2005
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In many cases the preparation of the initial state is difficult and an efficient algorithm may not be available.”
hedged- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As will be discussed later, these are not easy tasks, even for quantum simulators.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This results in an exponential growth of the statistical error, and hence the required simulation time, with the number of particles, which cancels the advantage of the Monte Carlo methods.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Unfortunately, in most cases of practical interest [ H l , H l ′ ] = 0 in general.”
plain- Asserted: fails — The authors may not put it forward as true.
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Probably not a substantial claim. The authors may not put it forward as true. The paper may give no reason why it holds.
- The authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.
In the paper
“Classical stochastic methods, namely Monte Carlo algorithms (Suzuki, 1993), have been developed as a way of tackling the difficult problem of simulating large quantum systems.”
What the sources say
- Not checked yetcites Suzuki, 1993
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The Hamiltonian of the system to be simulated, H sys , is directly mapped onto the Hamiltonian of the simulator, H sim , which can be controlled at least to some extent:”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Since any unitary operation can be written in terms of universal quantum gates, it follows that in principle 'anything' can be simulated, i.e. DQS is universal (Lloyd, 1996).”
What the sources say
- Not checked yetcites Lloyd, 1996
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In other words, although not all mathematically allowed Hamiltonians can be simulated efficiently, those that appear in most physical theories can be simulated efficiently.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, it must be noted that not any unitary operation can be efficiently simulated (that is with polynomial resources) and, therefore, there are Hamiltonians that cannot be efficiently simulated in this way.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“The topic was further discussed in (Poulin et al. , 2011) where it was shown that using randomness, it is possible to efficiently simulate local bounded Hamiltonians with arbitrary time dependence.”
What the sources say
- Not checked yetcites Poulin et al., 2011
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In principle, this approximation can be made arbitrarily accurate (by refining the decomposition), but this comes at the cost of an ever-increasing number of gates.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“This procedure provides an arbitrarily accurate estimate of the energy, with the accuracy increasing with increasing number of iterations.”
What the sources say
- Not checked yetcites Aspuru-Guzik et al., 2005
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
In the paper
“Moreover, according to (Meyer, 2002) it should also be possible to use quantum computers to simulate classical physics more efficiently (see also (Sinha and Russer, 2010; Yung et al. , 2010)).”
What the sources say
- Not checked yetcites Meyer, 2002
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, a few imperfections in an ensemble of particles performing AQS might not affect the overall behavior of the ensemble, such that the AQS might still produce useful results even in the presence of these imperfections.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that the simulator may only partly reproduce the dynamics of the system.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If the quantum simulator suffers from uncertainties in the control parameters, the phase transition under study could still be observed, hence providing the answer to the question of interest.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The choice of the mapping depends on what needs to be simulated and on the capabilities of the simulator.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“As discussed in the previous sections, fully characterizing a quantum system requires an exponentially large number of parameters.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“so chemical dynamics could be simulated on a quantum computer in O ( N 2 m 2 ) steps, which is exponentially faster than known classical algorithms.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The analog simulation of the BoseHubbard model using atoms in optical lattices is therefore straightforward.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The estimation of the requirements for simulating N particles interacting through a pairwise potential has been performed in (Kassal et al. , 2008).”
What the sources say
- Not checked yetcites Kassal et al. , 2008
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although quantum simulators are affected by the interactions with the environment in the same way as quantum computers, it is generally believed that the effects of decoherence are less dramatic.”
hedged- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Sometimes the mapping is indeed straightforward, but this is not always the case, and quite often clever mappings have to be devised, sometimes involving additional externally applied fields or ancillary systems to mediate various interactions.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Moreover, directly measuring some physical quantity of the simulator would yield information about its analogue in the simulated system.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper may give no reason why it holds.
- The authors state this as an assumption: The simulated system and its simulator are very similar.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finding the mapping in an AQS might, at first glance, look simpler than obtaining the most efficient gate decomposition for a given Hamiltonian in DQS.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“With a few tens of qubits, one could perform frustrated-spin simulations or molecular-energy calculations at the limits of present-day supercomputers.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“By analyzing the Ising model as a representative example, and using parameters that are relevant to present-day experiments, the authors concluded that surface codes are superior for quantum simulation.”
What the sources say
- Not checked yetcites You et al. , 2013
boosted- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The amount of physical resources (i.e., number of qubits, number of operations, number of steps, etc.) needed for the quantum simulation in the case of an N -body problem strongly depends on the type of problem and the particularities of the simulator.”
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“As a general rule of thumb, it is sometimes said that in order to outperform classical computers quantum simulators require somewhere between 40 and 100 qubits (Buluta and Nori, 2009).”
What the sources say
- Not checked yetcites Buluta and Nori, 2009
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This new class of algorithms makes it possible to simulate spin systems for longer times, and to study physical phenomena which would have been inaccessible with previous methods.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In AQS one is usually emulating an effective many-body model of the simulated system. A controllable 'toy-model' of the system is used to reproduce the property of interest, e.g. the dynamics or ground state.”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Its quantum version allows for the direct sampling from the eigenstates of the Hamiltonian, overcoming in this way the sign problem (Temme et al. , 2011).”
What the sources say
- Not checked yetcites Temme et al. , 2011
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“Moreover, it has been suggested that the decoherence of the simulator might be useful (Lloyd, 1996) as it could serve as a rough way of modeling the decoherence of the simulated system.”
What the sources say
- Not checked yetcites Lloyd, 1996
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Moreover, quantum dots allow flexible control over the confinement potential and they can also be excited optically.”
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Electron spins in quantum dots may provide an advantage over atoms in optical lattices due to the very low temperatures (relative to the Fermi temperature) that can be reached and the natural long-range Coulomb interaction.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The physical implementation of a quantum simulator requires a controllable quantum mechanical system.”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, it is not very flexible and its main disadvantage is the lack of scalability, one of the main reasons being the spectral crowding that occurs as the number of energy levels increases exponentially with increasing number of spins.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For many problems in this class, an array of qubits plus their controls (see Figure 8) would make an ideal quantum simulator because it can be thought of as the simplified, magnified lattice structure of a 'solid', that can be manipulated in a number of different ways in order to test various models.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Ion qubits also have long coherence times of the order of seconds, and sequences of high-fidelity quantum gates have been demonstrated in experiment (Hanneke et al. , 2009; Lanyon et al. , 2011).”
What the sources say
- Not checked yetcites Hanneke et al. , 2009
- Not checked yetcites Lanyon et al. , 2011
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using RF pulses various one-, two- and possibly multi-qubit gates can be implemented.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Crossvalidation over a number of different physical systems could be used, and in this way the particular imperfections of each implementation could be ruled out as possible sources of error.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
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Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Indeed, optical lattices provide the highly desirable properties of being easily tunable and essentially defect-free.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Alternative systems that can be used for quantum simulation include Rydberg atoms (Weimer et al. , 2010) and polar molecules (Lewenstein, 2006; Micheli et al. , 2006).”
What the sources say
- Not checked yetcites Weimer et al. , 2010
- Not checked yetcites Lewenstein, 2006
- Not checked yetcites Micheli et al. , 2006
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Nuclear spins manipulated by means of NMR have been among the first experimental systems to implement small quantum algorithms and quantum simulation (Li et al. , 2011; Peng and Suter, 2010; Peng et al. , 2009; Zhang et al. , 2012).”
What the sources say
- Not checked yetcites Li et al. , 2011
- Not checked yetcites Peng and Suter, 2010
- Not checked yetcites Peng et al. , 2009
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Nevertheless, nuclear spins provide a very good testbed for various small simulation problems and allow the implementation of both DQS and AQS.”
boosteddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Any physical system that can be used as a quantum computer would also be a universal machine for DQS.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If the region is roughly the same size as the wavelength of the charge carrier, the energy levels are quantized and the quantum dot becomes very similar to a real atom (and can therefore be referred to as an 'artificial atom').”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Ions can be trapped by electric (or magnetic) fields, laser-cooled and manipulated with high precision for realizing quantum simulation (Blatt and Wineland, 2008; Johanning et al. , 2009; Sch¨ atz et al. , 2007, 2004).”
What the sources say
- Not checked yetcites Blatt and Wineland, 2008
- Not checked yetcites Johanning et al. , 2009
- Not checked yetcites Sch¨ atz et al. , 2007, 2004
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“several groups have observed signatures of the crossover between a BCS and a BEC superfluid as the strength of attractive interactions between fermionic particles is varied”
What the sources say
- Not checked yetcites Regal et al. , 2004
- Not checked yetcites Zwierlein et al. , 2005
- Not checked yetcites Lewenstein et al. , 2007
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The frequencies can also be tuned in situ by adjusting an external parameter (typically an external magnetic field), and the coupling energy between two qubits can be turned on and off at will.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Photons can carry quantum information over long distances, hardly being affected by noise or decoherence.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The Hubbard model is the simplest model of interacting particles on a lattice. However, for large numbers of particles in more than one dimensions, the model is difficult to treat using classical computers.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In general, with a quantum simulator one could address problems that are either intractable on classical computers or experimentally challenging .”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Currently only with neutral atoms in an optical lattice is it possible to perform quantum simulations with more than a few particles, and these systems can at present be considered the most advanced platform for AQS.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“They naturally possess the ability to encode qubit states, e.g. in the polarization of the photon, and one-qubit gates can be easily realized with linear optical components.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“it has been simulated with a trapped ion (Gerritsma et al. , 2010).”
What the sources say
- Not checked yetcites Gerritsma et al. , 2010
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Rests on an assumption: Zitterbewegung has never been observed in its original form with free relativistic particles.
In the paper
“Another system that could be used for the quantum simulation of condensed matter physics is electrons trapped on the surface of liquid helium (Mostame and Sch¨ utzhold, 2008). This setup could be used to simulate the Ising model.”
What the sources say
- Not checked yetcites Mostame and Sch¨ utzhold, 2008
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“A recent experiment (L¨ ahteenm¨ aki et al. , 2013) used a superconducting circuit to simulate a massless Klein-Gordon field with tunable speed of propagation, which was used to simulate the generation of photons in the dynamical casimir effect.”
What the sources say
- Not checked yetcites L¨ ahteenm¨ aki et al. , 2013
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“A quantum simulation of this phenomenon was recently implemented with trapped ions (Gerritsma et al. , 2011).”
What the sources say
- Not checked yetcites Gerritsma et al. , 2011
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Furthermore, superconducting circuits can be coupled to 'cavities', which are actually electrical resonators (and the 'photons' are, for the most part, electron-density oscillations). This setup is very useful for the study of electric-circuit analogues of cavity quantum electrodynamics (circuit QED) (Schoelkopf and Girvin, 2008; You and Nori, 2005, 2011).”
What the sources say
- Not checked yetcites Schoelkopf and Girvin, 2008
- Not checked yetcites You and Nori, 2005, 2011
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although macroscopic in size, these circuits can display quantum behavior and can be seen as 'artificial atoms'.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Unlike other systems studied in the context of quantum computation, however, NV centers in diamond have not received much attention as potential quantum simulators, which might be due to difficulties in coupling the NV centers to each other and future scalability.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“it is also possible to simulate classically the Zitterbewegung of a free Dirac electron in an optical superlattice (Dreisow et al. , 2010).”
What the sources say
- Not checked yetcites Dreisow et al. , 2010
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In principle it could be scaled up, but the control would be very difficult.”
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although the difficulty in implementing two-qubit gates is a serious drawback for photonic systems in the context of quantum computation, there have been some notable achievements for quantum simulation using photons.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Quantum information can be encoded in different ways: in the number of superconducting electrons on a small island, in the direction of a current around a loop, or in oscillatory states of the circuit.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Both have discrete energy levels and exhibit coherent quantum oscillations between those levels.”
What the sources say
- Not checked yetcites You and Nori, 2005, 2011
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
In the paper
“the quantum baker's map, a prototypical example in quantum chaos, has an efficient realization in terms of quantum gates (Schack, 1998).”
What the sources say
- Not checked yetcites Schack, 1998
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“In (Aspuru-Guzik et al. , 2005) it was shown how to compute molecular energies using DQS and the required number of qubits was estimated (see also Figure 4).”
What the sources say
- Not checked yetcites Aspuru-Guzik et al. , 2005
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Simulating the dynamics of open quantum systems is even more costly than that of closed quantum systems because solving the Lindblad equation requires quadratically more resources than solving the Schr¨ odinger equation for the same physical system.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“In (Piilo and Maniscalco, 2006) it was theoretically shown that a driven harmonic oscillator can act as a quantum simulator for the non-Markovian damped harmonic oscillator.”
What the sources say
- Not checked yetcites Piilo and Maniscalco, 2006
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Another recent experiment simulated non-markovian Dynamics using a linear-optics setup (Chiuri et al. , 2012).”
What the sources say
- Not checked yetcites Chiuri et al. , 2012
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Simulating open quantum systems with quantum simulators can be done in two ways.”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“More recently, chemical reaction dynamics have been investigated using NMR DQS (Lu et al. , 2011).”
What the sources say
- Not checked yetcites Lu et al. , 2011
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“A simulation of decoherence caused by classical noise that was artificially added to the control signal of a superconducting qubit was reported in (Li et al. , 2013).”
What the sources say
- Not checked yetcites Li et al. , 2013
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“A recent experiment with trapped ions demonstrated the possibility of engineering open-system dynamics using the dissipative preparation of entangled states (Barreiro et al. , 2011).”
What the sources say
- Not checked yetcites Barreiro et al. , 2011
boosteddirectSingle case- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The algorithm would run in polynomial time while any exact classical simulation is bound to exhibit exponential scaling.”
What the sources say
- Not checked yetcites Lidar and Wang, 1999
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“The authors showed how a quantum dot with one electron can be considered an artificial hydrogen atom and a quantum dot containing four electrons can be viewed as an artificial oxygen atom.”
What the sources say
- Not checked yetcites Smirnov et al. , 2007
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“But whereas natural atoms are driven using visible or microwave photons that excite electrons from one state to another, the artificial atoms in the circuits are driven by currents, voltages, and microwave photons.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Differences between quantum circuits and natural atoms include how strongly each system couples to its environment (the coupling is weak for atoms and strong for circuits) and the energy scales of the two systems.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“an efficient algorithm for calculating the thermal rate constant was given in (Lidar and Wang, 1999).”
What the sources say
- Not checked yetcites Lidar and Wang, 1999
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The molecular energies of the hydrogen molecule have been calculated using a small photonic DQS (Lanyon et al. , 2010).”
What the sources say
- Not checked yetcites Lanyon et al. , 2010
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The number of qubits scales linearly with the number of basis functions, and the number of gates grows polynomially with the number of qubits, so simulations with a few tens or a hundred qubits would already outperform classical computers.”
What the sources say
- Not checked yetcites Aspuru-Guzik et al. , 2005
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These latter phenomena can be realized using quasi-one-dimensional open systems where photons are injected from one side and move towards the opposite side of the device.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“for some problems where bulk properties are of interest, individual control and measurement may not be required”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
In the paper
“it was shown that six to ten qubits would be sufficient for a simulation of the single-particle Schr¨ odinger equation.”
What the sources say
- Not checked yetcites Benenti and Strini, 2008
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The demonstration of quantum simulations using more than a few tens of qubits would mark the point where quantum computers (whether digital or analog) surpass their classical counterparts, at least for certain applications.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Several phenomenological models have been developed, one of which is the superfluid model of the atomic nucleus.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Progress on the experimental implementation of quantum simulation would also be relevant for measurement-based quantum computation.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“adiabatic quantum computation can be viewed as a special case of quantum simulation where the ground state of the simulated Hamiltonian encodes the solution to a computational problem”
What the sources say
- Not checked yetcites Farhi et al. , 2001
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From the experimental point of view, in all proposed quantum simulators improved controllability and scalability are required.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Even though N is not as large as in condensed matter physics (in this case N , the atomic mass number, is smaller than 300), the calculation of the nuclear force is difficult and therefore nuclear physics simulations require significant computing power.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Several recent experiments have demonstrated boson sampling using photons (Broome et al. , 2013; Crespi et al. , 2013; Spring et al. , 2013; Tillmann et al. , 2013)”
What the sources say
- Not checked yetcites Broome et al. , 2013
- Not checked yetcites Crespi et al. , 2013
- Not checked yetcites Spring et al. , 2013
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“These qubits, operating as tunable mirrors, can change the reflection and transmission coefficients of photons confined in waveguides.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Recent theoretical and experimental results on quantum simulation lead us to believe that practical quantum simulators will be built in the near future.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
- Rests on an assumption: Current theoretical and experimental progress in quantum simulation will continue at a pace sufficient to build practical quantum simulators in the near future.
None of the sources cited for this claim have been checked yet.
In the paper
“Superconducting qubits can be used, for example, to perform Landau-Zener-St¨ uckelberg interferometry (Shevchenko et al. , 2010) and Fano and Fabry-Perot interferometry (Ian et al. , 2009; Liao et al. , 2010; Zhou et al. , 2008a).”
What the sources say
- Not checked yetcites Shevchenko et al. , 2010
- Not checked yetcites Ian et al. , 2009
- Not checked yetcites Liao et al. , 2010
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Along the way, the photons interact with either one or two qubits acting as tunable mirrors, controlled by changing the applied electric and/or magnetic fields on the qubits.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Boson sampling (Aaronson and Arkhipov, 2011) is another interferometry problem that is closely related to quantum simulation.”
What the sources say
- Not checked yetcites Aaronson and Arkhipov, 2011
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Some recent topics in physics research, such as Majorana fermions (Casanova et al. , 2011; You et al. , 2011), graphene (Gibertini et al. , 2009) or neutrino oscillations (Noh et al. , 2012) are now discussed in the context of quantum simulation.”
What the sources say
- Not checked yetcites Casanova et al. , 2011
- Not checked yetcites You et al. , 2011
- Not checked yetcites Gibertini et al. , 2009
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“This was among the first experimental realizations of quantum simulation.”
What the sources say
- Not checked yetcites Leibfried et al. , 2002
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Nonlinear interferometers were first investigated in trapped-ion experiments (Leibfried et al. , 2002).”
What the sources say
- Not checked yetcites Leibfried et al. , 2002
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It should exhibit observable interesting behavior even with only eight qubits.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
None of the sources cited for this claim have been checked yet.
In the paper
“The quantum baker's map has been experimentally realized in NMR (Weinstein et al. , 2002) and with linear optics (Howell and Yeaze, 2000).”
What the sources say
- Not checked yetcites Weinstein et al. , 2002
- Not checked yetcites Howell and Yeaze, 2000
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“The possibility of simulating the Schr¨ odinger equation on a DQS was first discussed in 1996 (Lloyd, 1996), with concrete algorithms given in 1998 (Boghosian and Taylor, 1998a), where a quantum lattice-gas model for the many-particle Schr¨ odinger equation in d dimensions was proposed.”
What the sources say
- Not checked yetcites Lloyd, 1996
- Not checked yetcites Boghosian and Taylor, 1998a
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The authors state this as an assumption.
The Hamiltonian can be written as a sum of many terms that describe local interactions.
“We assume that the Hamiltonian can be written as a sum of many terms that describe local interactions:”
The authors state this as an assumption.
There is no restriction in applying one- and two-qubit gates and all qubits of the simulator can be individually addressed and measured.
“Furthermore, it is usually assumed that there is no restriction in applying one- and two-qubit gates and that all qubits of the simulator can be individually addressed and measured.”
The authors state this as an assumption.
The simulated system and its simulator are very similar.
“Because the system and simulator are presumed to be very similar”
The authors state this as an assumption.
The Lamb-Dicke parameter η is small.
“η is the Lamb-Dicke parameter (which is assumed to be small here)”
The paper relies on this without support.
Initial-state preparation and measurement in AQS have not been thoroughly discussed in the literature.
“The initial-state preparation and measurement in AQS have not been thoroughly discussed in the literature.”
The paper relies on this without support.
Less attention has been paid in the literature to the scaling of required resources with desired accuracy than to scaling with system size.
“Compared with the studies on scaling with the system size, less attention has been paid in the literature to the scaling of required resources with desired accuracy.”
The paper relies on this without support.
There has not been much work in the literature on resource estimation for AQS.
“There has not been much work in the literature on resource estimation for AQS.”
The paper relies on this without support.
So far there are few studies investigating how the simulator's imperfections affect the quantum simulation.
“So far there are few studies investigating how the simulator's imperfections affect the quantum simulation”
The authors state this as an assumption.
The Hamiltonian given for N charge or flux qubits biased at their symmetry points and coupled capacitively or inductively is valid for describing superconducting-circuit quantum simulators.
“The Hamiltonian for N charge (flux) qubits biased at their symmetry points (which is optimal for quantum coherence) coupled capacitively (inductively) is:”
The authors state this as an assumption.
The Hubbard Hamiltonian given is valid for describing the Fermi-Hubbard model.
“In (Somma et al. , 2002) it was shown how to obtain the energy spectrum of the Fermi-Hubbard Hamiltonian:”
The authors state this as an assumption.
The spin Hamiltonian form given is valid for describing spin systems.
“Spin systems are typically described by Hamiltonians of the form”
The authors state this as an assumption.
The quantum Ising model Hamiltonian given is valid for describing the trapped-ion quantum magnet simulation.
“The system is described by the quantum Ising model. The Hamiltonian for a chain (with two or more spins) is given by”
The authors state this as an assumption.
The Fano-Anderson Hamiltonian given is valid for describing the fermionic Fano-Anderson model.
“The Fano-Anderson Hamiltonian can be written as follows:”
The paper relies on this without support.
Current theoretical and experimental progress in quantum simulation will continue at a pace sufficient to build practical quantum simulators in the near future.
“Recent theoretical and experimental results on quantum simulation lead us to believe that practical quantum simulators will be built in the near future.”
The paper relies on this without support.
Zitterbewegung has never been observed in its original form with free relativistic particles.
“Zitterbewegung has never been observed in its original form with free relativistic particles”
The paper relies on this without support.
The simulation of gauge theories is a very computationally intensive quantum many-body problem.
“The simulation of gauge theories can be a very computationally intensive quantum many-body problem”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“the most important early application of quantum computers is likely to be the simulation of quantum systems. 40 -42”
From Quantum algorithms: an overview (2016) · cites this paper as [42]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“and quantum simulations have now been implemented, in some form, on essentially every technological platform for quantum computing.”
From Quantum algorithms: an overview (2016) · cites this paper as [42]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Several devices that are publicized in the name 'quantum simulation' are, in fact, analog simulators [63-67].”
From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [67]
In the citing paper
“Fortunately, this synergy has been amplified by the development of software platforms such as Rigetti's pyQuil 389 , IBM's QISKit 390 , ETH Z¨ urich's ProjectQ 391 , Google's Cirq 392 , and Xanadu's Strawberry Fields 393 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [390]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated major: it would touch a result — a value a result rests on, reported and recomputed p-values on opposite sides of the significance level, two passages that conflict with no sign which is right, or a cited work retracted before this paper was published.
In the paper
§ F. Current state of the art · p. 17
“Currently only with neutral atoms in an optical lattice is it possible to perform quantum simulations with more than a few particles”
§ A. Atoms and ions · p. 14
“In fact a two-dimensional ion array was recently used to implement a quantum simulation of a spin system with hundreds of ions (Britton et al. , 2012).”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ F. Current state of the art · p. 18
“As for the inter-ion distances in ion trap arrays, they are about 10-50 µ m and about the same for two-dimensional Coulomb crystals.”
§ F. Current state of the art · p. 18
“These inter-qubit distances (from 0.1 to 10 µ m) are to be compared with the far smaller average inter-atomic distances in solids, which are ≤ 1 nm.”
Citations
Cites
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
Many-body physics with ultracold gases
Bloch, I., Dalibard, J., & Zwerger, W. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.885 · Cited by 8,114 · cited 1×
“Other reviews (Bloch et al., 2012, 2008) describe recent experimental progress.”
BackgroundSimulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238 · cited 3×
“…have a positive impact on the development of other fields such as adiabatic quantum computation (Farhi et al., 2001), measurement-based quantum computation (Raussendorf et al., 2003), topological quantum computation (Kitaev, 2003) and the theory of quantum computation (Vollbrecht and Cirac, 2008).”
BackgroundMethodKimble, H. J. (2008) · Nature · doi:10.1038/nature07127 · Cited by 6,023 · cited 2×
“, 2006) could also be used as quantum simulators (see also (Kimble, 2008)).”
BackgroundQuantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., & Bloch, I. (2002) · Nature · doi:10.1038/415039a · Cited by 5,935 · cited 15×
“interaction energy was controlled in (Greiner et al., 2002) by adjusting the lattice potential depth, such that the quantum”
BackgroundMethodInfluentialChiral tunnelling and the Klein paradox in graphene
Katsnelson, M. I., Novoselov, K. S., & Geim, A. K. (2006) · Nature Physics · doi:10.1038/nphys384 · Cited by 3,896 · cited 1×
“A proposal for a simulation using graphene was put forward in (Katsnelson et al., 2006).”
MethodStrong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics
Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Huang, R. S., Majer, J., Kumar, S., Girvin, S. M., & Schoelkopf, R. J. (2004) · Nature · doi:10.1038/nature02851 · Cited by 3,796
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Cold Bosonic Atoms in Optical Lattices
Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W., & Zoller, P. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3108 · Cited by 3,685 · cited 8×
“Hubbard models Atoms (Jaksch et al., 1998),(Greiner et al.”
MethodInfluential
Research works printed but not linked: 4
- Aaronson, S., 2011, Proceedings of the 43rd Annual ACM Symposium on Theory of Computing
- Manin, Y., 1980, Computable and Uncomputable
- Porras, D., 2005, Laser Phys., 15, 88
- 10.1007/s11128-011-0303-5 · DOI
Cited by
Sorted by citations
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
A quantum engineer's guide to superconducting qubits
Krantz, P., Kjærgaard, M., Yan, F., Orlando, T. P., Gustavsson, S., & Oliver, W. D. (2019) · Applied Physics Reviews · doi:10.1063/1.5089550 · Cited by 2,321
Quantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621
Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems
Xiang, Z.-L., Ashhab, S., You, J. Q., & Nori, F. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.623 · Cited by 1,514
Self-citationSearch for new physics with atoms and molecules
Safronova, M. S., Budker, D., DeMille, D. P., Kimball, D. F. J., Derevianko, A., & Clark, C. W. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.025008 · Cited by 1,642
Metadata
- Authors
- Georgescu, I. M., Ashhab, S., & Nori, F.
- Affiliations
- RIKEN (JP)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2014-03-10
- Volume
- 86
- Issue
- 1
- Pages
- 153-185
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W3037443854
- Semantic Scholar
- 29fef61b3d7c3fcbd70e5055c17743173e317d67
- Cited by
- 2,932
- References
- 398
- Citations by year
- 2026: 195 · 2025: 320 · 2024: 324 · 2023: 313 · 2022: 302 · 2021: 308 · 2020: 242 · 2019: 243 · 2018: 197 · 2017: 145 · 2016: 146 · 2015: 119 · 2014: 58
- FWCI
- 77.73
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Army Research Office
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum simulation, quantum simulators, quantum computing hardware, analog quantum simulation, quantum many-body systems, trapped ions, neutral atoms, polar molecules, superconducting circuits, nuclear spin, quantum chemistry, condensed matter physics
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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