Quantum simulation

Probably not a substantial claim: may not pass S3 (load-bearing).

In a recent experiment, the predictions of the two-dimensional Mott-Hubbard model were tested for electrons in an artificial honeycomb lattice.

“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).”

• cites Singha et al. , 2011Not checked yet

  Not checked in the free run.

May combine two claims.

Circuits containing 512 qubits have been fabricated, 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.

“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.”

• cites Harris, 2012Not checked yet

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• cites Harris et al. , 2010Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Corresponding experiments with up to four photons were performed.

“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).”

• cites Broome et al. , 2013Not checked yet

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• cites Crespi et al. , 2013Not checked yet

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• cites Spring et al. , 2013Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

The quantum phase transition from a superfluid to a Mott insulator phase, predicted in (Fisher et al., 1989), was first observed in 2002 in an ensemble of atoms trapped in an optical lattice.

“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.”

• cites Fisher et al. , 1989Not checked yet

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• cites Greiner et al. , 2002Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

An AQS of the Bose-Hubbard model using atoms in optical lattices was proposed and implemented.

“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).”

• cites Jaksch et al. , 1998Not checked yet

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• cites Greiner et al. , 2002Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

More than 200 superconducting resonators were recently fabricated on a single chip.

“Furthermore, more than 200 superconducting resonators were recently fabricated on a single chip (Houck et al. , 2012).”

• cites Houck et al. , 2012Not checked yet

  Not checked in the free run.

May combine two claims.

Photons have been used to calculate the possible fractional statistics of anyons using a six-photon graph state, to calculate the energy spectrum of the hydrogen molecule to 20 bits of precision, and to simulate frustrated spin systems.

“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).”

• cites Lu et al. , 2009Not checked yet

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• cites Lanyon et al. , 2010Not checked yet

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• cites Ma et al. , 2011Not checked yet

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Classified as probably not a substantial claim. May combine two claims.

State-of-the-art superconducting qubits have coherence times exceeding 100 μs, 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 to 10 GHz.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Optical lattices have been used to experimentally realize a disordered system that may lead to the observation of a Bose glass phase.

“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).”

• cites Fallani et al. , 2007Not checked yet

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May combine two claims.

In trapped-ion DQS 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.

“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.”

• cites Lanyon et al. , 2011Not checked yet

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Probably not a substantial claim: may not pass S4 (based).

Individual control and readout are difficult to realize for atoms in optical lattices.

“individual control and readout are difficult to realize for atoms in optical lattices”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

For other systems, individual control and readout are not a problem.

“while for other systems that is not a problem”

Probably not a substantial claim: may not pass S4 (based).

With the exception of atoms in optical lattices, quantum simulators cannot yet handle large arrays of qubits.

“With the exception of atoms in optical lattices, quantum simulators cannot yet handle large arrays of qubits.”

May combine two claims.

A quantum machine would have the capacity to contain an exponentially large amount of information without using an exponentially large amount of physical resources, making it a natural tool to perform quantum simulation.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control and therefore be easier to construct.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Other potential application areas of quantum simulation include high-energy physics, quantum chemistry, cosmology and nuclear physics.

“Other potential application areas include highenergy physics, quantum chemistry, cosmology and nuclear physics.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

With the latest advances in the coherent manipulation of quantum systems, practical applications of quantum simulation can be expected in the coming years.

“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.”

• cites Buluta et al., 2011Not checked yet

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• cites Ladd et al., 2010Not checked yet

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May combine two claims.

Depending on the specifics of the problem, good approximations are not always available or they also face limitations.

“However, depending on the specifics of the problem under study, good approximations are not always available or they also face some limitations.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Quantum simulation promises to have applications in the study of many problems in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology.

“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.”

Classified as probably not a substantial claim.

The difficulty of simulating quantum mechanics may be overcome by using a controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation.

“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.”

Classified as probably not a substantial claim.

Quantum simulation would allow the study of many difficult problems in condensed-matter physics, such as quantum phase transitions, quantum magnetism or high-Tc superconductivity.

“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.”

May combine two claims.

Simpler quantum devices that mimic the evolution of other quantum systems in an analog manner could be used for quantum simulation, though they are problem-specific and not universal simulators.

“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).”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

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.

“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.”

May combine two claims.

Ancilla qubits are required for simulating many-body interactions, which adds to the resource requirements.

“Moreover, note that ancilla qubits are required, which adds to the resource requirements (see Section V. B).”

• AssumptionThe 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.

Classified as probably not a substantial claim.

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.

“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.”

May combine two claims.

Several methods have been developed for efficient simulation of many-body interactions using two-body interactions, but it still remains a difficult problem.

“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.”

• cites Berry et al., 2007Not checked yet

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• cites Bravyi et al., 2008Not checked yet

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• cites Bremner et al., 2005Not checked yet

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• AssumptionThe 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.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

In many cases the preparation of the initial state is difficult and an efficient algorithm may not be available.

“In many cases the preparation of the initial state is difficult and an efficient algorithm may not be available.”

• AssumptionThe 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.

Classified as probably not a substantial claim.

Initial state preparation, implementation of time evolution and measurement are not easy tasks, even for quantum simulators.

“As will be discussed later, these are not easy tasks, even for quantum simulators.”

May combine two claims.

The sign problem 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 Monte Carlo methods.

“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.”

Probably not a substantial claim: may not pass S1 (asserted), S4 (based).

In most cases of practical interest, [H_l, H_l'] ≠ 0 in general.

“Unfortunately, in most cases of practical interest [ H l , H l ′ ] = 0 in general.”

• AssumptionThe authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.

Probably not a substantial claim: may not pass S3 (load-bearing).

Classical stochastic methods, namely Monte Carlo algorithms, have been developed as a way of tackling the difficult problem of simulating large quantum systems.

“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.”

• cites Suzuki, 1993Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

In AQS, the Hamiltonian of the system to be simulated is directly mapped onto the Hamiltonian of the simulator, which can be controlled at least to some extent.

“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:”

May combine two claims.

DQS is universal in principle because any unitary operation can be written in terms of universal quantum gates.

“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).”

• cites Lloyd, 1996Not checked yet

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• AssumptionThe 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.

May combine two claims.

Although not all mathematically allowed Hamiltonians can be simulated efficiently, those that appear in most physical theories can be simulated efficiently.

“In other words, although not all mathematically allowed Hamiltonians can be simulated efficiently, those that appear in most physical theories can be simulated efficiently.”

• AssumptionThe authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.

May combine two claims.

Not any unitary operation can be efficiently simulated with polynomial resources; therefore, there are Hamiltonians that cannot be efficiently simulated by DQS.

“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.”

• AssumptionThe 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.

Probably not a substantial claim: may not pass S3 (load-bearing).

Using randomness, it is possible to efficiently simulate local bounded Hamiltonians with arbitrary time dependence.

“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.”

• cites Poulin et al., 2011Not checked yet

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• AssumptionThe authors state this as an assumption: The Hamiltonian can be written as a sum of many terms that describe local interactions.
• AssumptionThe 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.

May combine two claims.

The approximation of the desired unitary evolution can in principle be made arbitrarily accurate by refining the decomposition, but this comes at the cost of an ever-increasing number of gates.

“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.”

• AssumptionThe 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.

May combine two claims.

The recursive phase-estimation algorithm of Aspuru-Guzik et al. (2005) provides an arbitrarily accurate estimate of molecular energy, with accuracy increasing with the number of iterations.

“This procedure provides an arbitrarily accurate estimate of the energy, with the accuracy increasing with increasing number of iterations.”

• cites Aspuru-Guzik et al., 2005Not checked yet

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• AssumptionThe 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.

Probably not a substantial claim: may not pass S3 (load-bearing).

According to Meyer (2002), it should also be possible to use quantum computers to simulate classical physics more efficiently.

“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)).”

• cites Meyer, 2002Not checked yet

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• AssumptionThe 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.

May combine two claims.

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The simulator in AQS may only partly reproduce the dynamics of the system.

“Note that the simulator may only partly reproduce the dynamics of the system.”

May combine two claims.

If the quantum simulator suffers from uncertainties in the control parameters, the phase transition under study could still be observed, providing the answer to the question of interest.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The choice of the mapping in AQS depends on what needs to be simulated and on the capabilities of the simulator.

“The choice of the mapping depends on what needs to be simulated and on the capabilities of the simulator.”

Probably not a substantial claim: may not pass S4 (based).

Fully characterizing a quantum system requires an exponentially large number of parameters.

“As discussed in the previous sections, fully characterizing a quantum system requires an exponentially large number of parameters.”

May combine two claims.

Chemical dynamics could be simulated on a quantum computer in O(N^2 m^2) steps, which is exponentially faster than known classical algorithms.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The analog simulation of the Bose-Hubbard model using atoms in optical lattices is straightforward.

“The analog simulation of the BoseHubbard model using atoms in optical lattices is therefore straightforward.”

Classified as probably not a substantial claim.

The estimation of the requirements for simulating N particles interacting through a pairwise potential has been performed in (Kassal et al., 2008).

“The estimation of the requirements for simulating N particles interacting through a pairwise potential has been performed in (Kassal et al. , 2008).”

• cites Kassal et al. , 2008Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

It is generally believed that the effects of decoherence are less dramatic for quantum simulators than for quantum computers.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Sometimes the mapping in AQS 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.

“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.”

Probably not a substantial claim: may not pass S4 (based).

Directly measuring some physical quantity of the simulator would yield information about its analogue in the simulated system.

“Moreover, directly measuring some physical quantity of the simulator would yield information about its analogue in the simulated system.”

• AssumptionThe authors state this as an assumption: The simulated system and its simulator are very similar.

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

With a few tens of qubits, one could perform frustrated-spin simulations or molecular-energy calculations at the limits of present-day supercomputers.

“With a few tens of qubits, one could perform frustrated-spin simulations or molecular-energy calculations at the limits of present-day supercomputers.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Surface codes are superior to circuit models with quantum error correction for fault-tolerant DQS.

“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.”

• cites You et al. , 2013Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The amount of physical resources needed for quantum simulation of an N-body problem strongly depends on the type of problem and the particularities of the simulator.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

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.

“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).”

• cites Buluta and Nori, 2009Not checked yet

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May combine two claims.

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In AQS, one usually emulates an effective many-body model of the simulated system, using a controllable toy-model to reproduce the property of interest, e.g., the dynamics or ground state.

“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.”

May combine two claims.

The quantum version of the Metropolis algorithm allows for direct sampling from the eigenstates of the Hamiltonian, overcoming the sign problem.

“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).”

• cites Temme et al. , 2011Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

The decoherence of the simulator might be useful as it could serve as a rough way of modeling the decoherence of the simulated system.

“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.”

• cites Lloyd, 1996Not checked yet

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May combine two claims.

Quantum dots allow flexible control over the confinement potential and can be excited optically.

“Moreover, quantum dots allow flexible control over the confinement potential and they can also be excited optically.”

Probably not a substantial claim: may not pass S3 (load-bearing).

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The physical implementation of a quantum simulator requires a controllable quantum mechanical system.

“The physical implementation of a quantum simulator requires a controllable quantum mechanical system.”

May combine two claims.

NMR is not very flexible and its main disadvantage is lack of scalability, one reason being spectral crowding that occurs as the number of energy levels increases exponentially with increasing number of spins.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

An array of qubits plus their controls would make an ideal quantum simulator for many condensed matter problems because it can be thought of as the simplified, magnified lattice structure of a solid.

“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.”

May combine two claims.

Ion qubits have long coherence times of the order of seconds, and sequences of high-fidelity quantum gates have been demonstrated in experiment.

“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).”

• cites Hanneke et al. , 2009Not checked yet

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• cites Lanyon et al. , 2011Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Using RF pulses, various one-, two- and possibly multi-qubit gates can be implemented in NMR.

“Using RF pulses various one-, two- and possibly multi-qubit gates can be implemented.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Cross-validation over a number of different physical systems could be used to rule out the particular imperfections of each implementation as possible sources of error.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Optical lattices provide the highly desirable properties of being easily tunable and essentially defect-free.

“Indeed, optical lattices provide the highly desirable properties of being easily tunable and essentially defect-free.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Alternative systems that can be used for quantum simulation include Rydberg atoms and polar molecules.

“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).”

• cites Weimer et al. , 2010Not checked yet

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• cites Lewenstein, 2006Not checked yet

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• cites Micheli et al. , 2006Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

Nuclear spins manipulated by means of NMR have been among the first experimental systems to implement small quantum algorithms and quantum simulation.

“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).”

• cites Li et al. , 2011Not checked yet

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• cites Peng and Suter, 2010Not checked yet

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• cites Peng et al. , 2009Not checked yet

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May combine two claims.

Nuclear spins provide a very good testbed for various small simulation problems and allow the implementation of both DQS and AQS.

“Nevertheless, nuclear spins provide a very good testbed for various small simulation problems and allow the implementation of both DQS and AQS.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Any physical system that can be used as a quantum computer would also be a universal machine for DQS.

“Any physical system that can be used as a quantum computer would also be a universal machine for DQS.”

May combine two claims.

If the confinement region of a quantum dot 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.

“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').”

May combine two claims.

Ions can be trapped by electric or magnetic fields, laser-cooled and manipulated with high precision for realizing quantum simulation.

“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).”

• cites Blatt and Wineland, 2008Not checked yet

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• cites Johanning et al. , 2009Not checked yet

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• cites Sch¨ atz et al. , 2007, 2004Not checked yet

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Probably not a substantial claim: may not pass S3 (load-bearing).

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.

“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”

• cites Regal et al. , 2004Not checked yet

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• cites Zwierlein et al. , 2005Not checked yet

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• cites Lewenstein et al. , 2007Not checked yet

  Not checked in the free run.

May combine two claims.

The frequencies of superconducting circuits can 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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Photons can carry quantum information over long distances, hardly being affected by noise or decoherence.

“Photons can carry quantum information over long distances, hardly being affected by noise or decoherence.”

Classified as probably not a substantial claim. May combine two claims.

The Hubbard model is the simplest model of interacting particles on a lattice, but for large numbers of particles in more than one dimension it is difficult to treat using classical computers.

“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.”

Classified as probably not a substantial claim.

In general, with a quantum simulator one could address problems that are either intractable on classical computers or experimentally challenging.

“In general, with a quantum simulator one could address problems that are either intractable on classical computers or experimentally challenging .”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Photons 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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Zitterbewegung has been simulated with a trapped ion.

“it has been simulated with a trapped ion (Gerritsma et al. , 2010).”

• cites Gerritsma et al. , 2010Not checked yet

  Not checked in the free run.

• AssumptionRests on an assumption: Zitterbewegung has never been observed in its original form with free relativistic particles.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Electrons trapped on the surface of liquid helium could be used for quantum simulation of condensed matter physics, and this setup could be used to simulate the Ising model.

“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.”

• cites Mostame and Sch¨ utzhold, 2008Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A recent experiment 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.

“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.”

• cites L¨ ahteenm¨ aki et al. , 2013Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

A quantum simulation of the Klein paradox was recently implemented with trapped ions.

“A quantum simulation of this phenomenon was recently implemented with trapped ions (Gerritsma et al. , 2011).”

• cites Gerritsma et al. , 2011Not checked yet

  Not checked in the free run.

May combine two claims.

Superconducting circuits can be coupled to cavities, which are electrical resonators, and this setup is useful for the study of electric-circuit analogues of cavity quantum electrodynamics (circuit QED).

“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).”

• cites Schoelkopf and Girvin, 2008Not checked yet

  Not checked in the free run.

• cites You and Nori, 2005, 2011Not checked yet

  Not checked in the free run.

May combine two claims.

Although macroscopic in size, superconducting circuits can display quantum behavior and can be seen as artificial atoms.

“Although macroscopic in size, these circuits can display quantum behavior and can be seen as 'artificial atoms'.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

It is possible to simulate classically the Zitterbewegung of a free Dirac electron in an optical superlattice.

“it is also possible to simulate classically the Zitterbewegung of a free Dirac electron in an optical superlattice (Dreisow et al. , 2010).”

• cites Dreisow et al. , 2010Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

In principle the liquid-helium electron system could be scaled up, but the control would be very difficult.

“In principle it could be scaled up, but the control would be very difficult.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The difficulty in implementing two-qubit gates is a serious drawback for photonic systems in the context of quantum computation.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Quantum information can be encoded in superconducting circuits 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.

“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.”

May combine two claims.

Both natural atoms and artificial atoms have discrete energy levels and exhibit coherent quantum oscillations between those levels.

“Both have discrete energy levels and exhibit coherent quantum oscillations between those levels.”

• cites You and Nori, 2005, 2011Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

The quantum baker's map has an efficient realization in terms of quantum gates.

“the quantum baker's map, a prototypical example in quantum chaos, has an efficient realization in terms of quantum gates (Schack, 1998).”

• cites Schack, 1998Not checked yet

  Not checked in the free run.

May combine two claims.

It was shown how to compute molecular energies using DQS and the required number of qubits was estimated.

“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).”

• cites Aspuru-Guzik et al. , 2005Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

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 Schrödinger equation for the same physical system.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

It was theoretically shown that a driven harmonic oscillator can act as a quantum simulator for the non-Markovian damped harmonic oscillator.

“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.”

• cites Piilo and Maniscalco, 2006Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Another recent experiment simulated non-Markovian dynamics using a linear-optics setup.

“Another recent experiment simulated non-markovian Dynamics using a linear-optics setup (Chiuri et al. , 2012).”

• cites Chiuri et al. , 2012Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Simulating open quantum systems with quantum simulators can be done in two ways.

“Simulating open quantum systems with quantum simulators can be done in two ways.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Chemical reaction dynamics have been investigated using NMR DQS.

“More recently, chemical reaction dynamics have been investigated using NMR DQS (Lu et al. , 2011).”

• cites Lu et al. , 2011Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

A simulation of decoherence caused by classical noise that was artificially added to the control signal of a superconducting qubit was reported.

“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).”

• cites Li et al. , 2013Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

A recent experiment with trapped ions demonstrated the possibility of engineering open-system dynamics using the dissipative preparation of entangled states.

“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).”

• cites Barreiro et al. , 2011Not checked yet

  Not checked in the free run.

May combine two claims.

The algorithm for calculating the thermal rate constant would run in polynomial time while any exact classical simulation is bound to exhibit exponential scaling.

“The algorithm would run in polynomial time while any exact classical simulation is bound to exhibit exponential scaling.”

• cites Lidar and Wang, 1999Not checked yet

  Not checked in the free run.

May combine two claims.

The authors of (Smirnov et al., 2007) 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.

“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.”

• cites Smirnov et al. , 2007Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Natural atoms are driven using visible or microwave photons that excite electrons from one state to another, whereas artificial atoms in circuits are driven by currents, voltages, and microwave photons.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Differences between quantum circuits and natural atoms include how strongly each system couples to its environment (weak for atoms, strong for circuits) and the energy scales of the two systems.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

An efficient algorithm for calculating the thermal rate constant was given in (Lidar and Wang, 1999).

“an efficient algorithm for calculating the thermal rate constant was given in (Lidar and Wang, 1999).”

• cites Lidar and Wang, 1999Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

The molecular energies of the hydrogen molecule have been calculated using a small photonic DQS.

“The molecular energies of the hydrogen molecule have been calculated using a small photonic DQS (Lanyon et al. , 2010).”

• cites Lanyon et al. , 2010Not checked yet

  Not checked in the free run.

May combine two claims.

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.

“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.”

• cites Aspuru-Guzik et al. , 2005Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

For some problems where bulk properties are of interest, individual control and measurement may not be required.

“for some problems where bulk properties are of interest, individual control and measurement may not be required”

Probably not a substantial claim: may not pass S3 (load-bearing).

It was shown that six to ten qubits would be sufficient for a simulation of the single-particle Schrödinger equation.

“it was shown that six to ten qubits would be sufficient for a simulation of the single-particle Schr¨ odinger equation.”

• cites Benenti and Strini, 2008Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S4 (based).

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.

“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.”

Classified as probably not a substantial claim. May combine two claims.

Several phenomenological models have been developed, one of which is the superfluid model of the atomic nucleus.

“Several phenomenological models have been developed, one of which is the superfluid model of the atomic nucleus.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Progress on the experimental implementation of quantum simulation would be relevant for measurement-based quantum computation.

“Progress on the experimental implementation of quantum simulation would also be relevant for measurement-based quantum computation.”

Probably not a substantial claim: may not pass S3 (load-bearing).

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.

“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”

• cites Farhi et al. , 2001Not checked yet

  Not checked in the free run.

Classified as probably not a substantial claim.

In all proposed quantum simulators, improved controllability and scalability are required.

“From the experimental point of view, in all proposed quantum simulators improved controllability and scalability are required.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Even though N is not as large as in condensed matter physics (N < 300), the calculation of the nuclear force is difficult and therefore nuclear physics simulations require significant computing power.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Several recent experiments have demonstrated boson sampling using photons.

“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)”

• cites Broome et al. , 2013Not checked yet

  Not checked in the free run.

• cites Crespi et al. , 2013Not checked yet

  Not checked in the free run.

• cites Spring et al. , 2013Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

These qubits, operating as tunable mirrors, can change the reflection and transmission coefficients of photons confined in waveguides.

“These qubits, operating as tunable mirrors, can change the reflection and transmission coefficients of photons confined in waveguides.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Recent theoretical and experimental results on quantum simulation lead us to believe that practical quantum simulators will be built 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.”

• AssumptionRests 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.

May combine two claims.

Superconducting qubits can be used to perform Landau-Zener-Stückelberg interferometry and Fano and Fabry-Perot interferometry.

“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).”

• cites Shevchenko et al. , 2010Not checked yet

  Not checked in the free run.

• cites Ian et al. , 2009Not checked yet

  Not checked in the free run.

• cites Liao et al. , 2010Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

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.

“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.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Boson sampling is another interferometry problem that is closely related to quantum simulation.

“Boson sampling (Aaronson and Arkhipov, 2011) is another interferometry problem that is closely related to quantum simulation.”

• cites Aaronson and Arkhipov, 2011Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Some recent topics in physics research, such as Majorana fermions, graphene or neutrino oscillations, are now discussed in the context of quantum simulation.

“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.”

• cites Casanova et al. , 2011Not checked yet

  Not checked in the free run.

• cites You et al. , 2011Not checked yet

  Not checked in the free run.

• cites Gibertini et al. , 2009Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

This was among the first experimental realizations of quantum simulation.

“This was among the first experimental realizations of quantum simulation.”

• cites Leibfried et al. , 2002Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Nonlinear interferometers were first investigated in trapped-ion experiments.

“Nonlinear interferometers were first investigated in trapped-ion experiments (Leibfried et al. , 2002).”

• cites Leibfried et al. , 2002Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The kicked Harper model should exhibit observable interesting behavior even with only eight qubits.

“It should exhibit observable interesting behavior even with only eight qubits.”