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Can one trust quantum simulators?
Open accessAbstract
Various fundamental phenomena of strongly correlated quantum systems such as high-T(c) superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by 'simulation' with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a 'quantum simulator,' would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question 'Can we trust quantum simulators?' is … to some extent.
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TL;DR
The paper argues that a useful quantum simulator must satisfy relevance, controllability, reliability, and efficiency, and reviews digital and analog implementations against these criteria. Using exact numerical simulations of a disordered transverse Ising chain, it finds that analog quantum simulators can be trusted “to some extent”: local observables are fairly robust to weak disorder, but global state fidelities, critical-point location, critical exponents, and central charge can be significantly corrupted.
Key findings
- The authors propose four requirements for a quantum simulator: relevance, controllability, reliability, and efficiency; they emphasize that reliability and efficiency have received much less attention than controllability.
- For a disordered transverse Ising chain with disorder strength \(r=0.1\) and \(L=400\) sites, the global simulator fidelity near the quantum phase transition drops as low as 55%, while local fidelities remain high: two-site fidelity \(f_2 \approx 0.998\) and single-site fidelity \(f_1 > 0.999\).
- Disorder shifts the extracted critical point to larger \(\lambda\), increases the apparent correlation-length exponent \(\nu\) above its ideal value 1, and decreases the effective central charge \(c\), so ignoring disorder can assign the transition to the wrong universality class.
- In dynamics, a local quench preserves high fidelity, but a global quench produces fidelities as low as 0.8 even for 50 spins; high-temperature initial states are more robust, with asymptotic infidelity scaling as \(1/T^2\), while low-temperature states are less reliable.
Methods
- The paper combines a conceptual review and classification of digital and analog quantum simulators with original numerical simulations of the one-dimensional transverse Ising model with quenched Gaussian disorder in both couplings \(J_{ij}=J(1+r\delta_{ij})\) and fields \(h_i=h(1+r\eta_i)\).
- The model is solved exactly via the Jordan-Wigner transformation to non-interacting fermions; the authors compute ground-state and time-dependent fidelities, reduced fidelities, correlations, energy gaps, critical exponents, and central charge.
- Static fidelities \(F\), \(f_1\), and \(f_2\) were averaged over 5000 disorder realizations at chain length \(L=400\); finite-size scaling used chain lengths up to \(L=400\) with varying numbers of disorder realizations.
Limitations
- The paper states that there exists no perfect and rigorous way to assess the reliability of analog quantum simulators, and that successful validation in a classically accessible regime does not guarantee robustness in classically inaccessible regimes.
- The study assumes quenched disorder as the only imperfection and explicitly leaves dynamical noise, decoherence, and environment coupling for future work; it also considers only small disorder strengths, allowing the Griffiths phase to be ignored.
- The transverse Ising model is exactly solvable and classically simulatable, so the authors describe the results as an initial attempt in a trivial model; evident limitations include the one-dimensional setting, finite-size pseudo-criticality, and the lack of direct demonstration for computationally hard models.
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67 Not checked yet · 41 Own interpretation · 38 No basis given · 32 Own result · 1 Supported · 1 Partly supported · accuracy not yet measured
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In the paper
“In accordance with [98], a UDQS is perfectly controllable, i.e., with the help of a universal set of gates sufficient control of the parameters can be achieved.”
What the sources say
- Supportedcites [98] source
The Toolbox for Digital Quantum Simulation (p. 3) describes a complete gate-based toolbox and says that choosing phases controls the relative interaction strengths. The Lattice Gauge Theory section (p. 5) explicitly says the digital implementation provides full control of spatial and temporal interaction strengths. This supports the citing sentence’s definition of controllability as sufficient parameter control, rather than error-free gates. (LLM, conf=0.86)
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“We find that disorder can decrease the reliability of an analog quantum simulator of this model”
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“although large errors in local observables are introduced only for strong levels of disorder.”
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“As can be seen, if one does not correct for disorder effects, one would locate the critical point at values of λ that are too large.”
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“As Fig. 1B shows, this overlap is considerably suppressed near the QPT, reaching values as low as 55% (for r = 0 . 1 in a chain of L = 400 sites).”
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“B: For a chain of 400 spins, we show the mean single- and two-site reduced simulator fidelities ( f 1 and f 2 ), and the total simulator fidelity ( F ) for a fixed disorder level r = 0 . 1 . Local fidelities are more robust, which gives hope that local quantities can be reliable even if disorder deteriorates the overall ground state.”
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“As expected, disorder has more severe effects close to the QPT.”
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“As shown in Fig. 1C, already for a few percent of disorder, ν increases strongly from its ideal value 1.”
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“The critical point (as extracted from a finite-size scaling of the energy gap ∆ ) moves to larger λ with increasing disorder (black line).”
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“We also observe that the AQS performs worse when the quench crosses the critical point, as shown in Fig. 2C, where we fix the strength of the quench and vary the initial field value.”
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- The authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.
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“Figure 1C shows that disorder decreases the effective central charge.”
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“For the models we have considered here, the physically relevant correlation functions are robust for a reasonable degree of disorder.”
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“Fortunately, for all the extracted quantities (except the global simulator fidelity), the levels of disorder for appreciable changes to occur are at least a few percent.”
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“For the regimes of disorder that we studied, we observe that the time dependent fidelity decays with a rate roughly proportional to the strength of the disorder squared (typical of a Fermi golden rule [191]).”
What the sources say
- Not checked yetcites [191] source
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“In terms of distinguishability, the values we find imply that a fair observer would have only a 4% chance of distinguishing the 1-spin reduced state of the AQS from the ideal state.”
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“As displayed in Fig. A1, the crossing point moves to larger values of λ with increasing disorder (see also Fig. 1A of the main text).”
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- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
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“For low disorder ( r = 0 , left), the curves 1 / ( L ∆( L )) cross perfectly at the location of the critical point, λ = 1 .”
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“Moreover, the qualitity of the collapse worsens with increasing disorder, demonstrating that a naive application of Eq. (A10) is unjustified if disorder is large.”
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“Figure A1 shows the best collapse achieved with Eq. (A10) for disorder levels r = 0 and 0 . 2 . The value of ν for the best collapse increases with disorder.”
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“In Fig. 1C of the main text, we show the erroneous values for ν , extracted from Eq. (A10) if one naively neglects that this relationship is no longer true in the presence of disorder.”
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“For low disorder ( r = 0 , left), the curves C ( i, j ) L 2 ν for different L plotted as functions of | i -j | /L collapse perfectly for the physically correct value of the critical exponent ν = 1 (dots of different color correspond to different L ).”
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“When such a digital quantum simulation operates with fault-tolerant quantum error correction [63], we can trust its output to a known finite precision.”
What the sources say
- Not checked yetcites [63] source
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“The number of resources needed for precise simulation of continuous-time dynamics of a many-body system by stroboscopic digital applications of local gates might be enormous [64].”
What the sources say
- Not checked yetcites [64] source
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“However, errors in an analog device (also continuous, like temperature in the initial state, or the signal-to-noise ratio of measurement) can propagate and multiply uncontrollably [58].”
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- Not checked yetcites [58] source
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“We conclude that the answer to the question 'Can we trust quantum simulators?' is... to some extent.”
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“Despite the fact that in such a case error correction and fault tolerance is guaranteed, the question of efficiency of such a device is highly non-trivial.”
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“The main obstacle is the computational complexity of solving even the most simplified theoretical models that are designed to capture the relevant quantum correlations of the many-body system of interest.”
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- Rests on an assumption: Various fundamental phenomena of strongly correlated quantum systems, such as high-Tc superconductivity, the fractional quantum-Hall effect, and quark confinement, are still awaiting a universally accepted explanation.
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“Real-world implementations of a quantum simulation will always face experimental imperfections, such as noise due to finite precision instruments and interactions with the environment.”
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“A UDQS is the only DQS which has guaranteed access to error correction and fault tolerance [107, 108]”
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“In 2D the situation is more complex - similar to exact diagonalization, DMRG and TTN work only for reasonably small systems [80-82]”
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“In the presence of errors, however, ensuring reliability to a desired precision has profound implications for efficiency even in a digital simulator on a fault-tolerant quantum computer [64, 117].”
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“The result is that a fault-tolerant implementation of the Trotter expansion requires a number of gates and time to perform the simulation that grows exponentially with the degree of precision required, for a fixed number of particles being simulated.”
What the sources say
- Not checked yetcites [64] source
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“On the other hand, for a fixed precision, the number of resources required grows weakly with system size.”
What the sources say
- Not checked yetcites [120] source
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“Quantum dynamics on a long time scale is generically computationally hard.”
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“So, if the error probability per gate can be reduced well below threshold to achieve the desired precision without many layers of concatenated error-correction encoding, then digital quantum simulation will scale favorably with the number of particles.”
What the sources say
- Not checked yetcites [120] source
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“Further, Preskill's group has proven recently that the scattering amplitudes in the simple relativistic quantum field theories can be efficiently (in polynomial time) simulated by UDQSs [105, 106].”
What the sources say
- Not checked yetcites [105] Nielsen M A, 2000, Quantum Computation and Quantum Information
- Not checked yetcites [106] source
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“since, e.g., sometimes giving up on universality can result in substantial efficiency gains.”
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“Lloyd who showed that any 'local' many-body unitary evolution governed by a 'local' Hamiltonian could be implemented by the control afforded by a universal digital quantum computer [98].”
What the sources say
- Not checked yetcites [98] source
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“Nevertheless, many experimental realizations should allow for a wide control of parameters, which in turn should allow for simulations of open-system (Markovian) evolutions for wide families of open systems of interest.”
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“However, there is no guarantee that such a calibration will hold in the truly interesting regimes of parameters, where efficient classical simulations are either impossible, or we do not know how to perform them.”
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“OSDQSs are typically not universal since they are not usually controllable in the sense of realizing an arbitrary quantum map [133].”
What the sources say
- Not checked yetcites [133] source
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“amazingly, in one case numerical simulations helped to correct the expected experimental temperature by up to 30% .”
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“This was recently demonstrated in experiments with ultracold bosonic and fermionic atoms [6-8];”
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“So far, there exists no perfect and rigorous way to assess the reliability of AQSs, but there are several complementary approaches.”
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“or that the quantum dynamics is in general computationally hard [96, 97].”
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“The efficiency of OSDQSs for the case of frustration-free Hamiltonians depends on the size of the gap between the ground state and the excited states, or more precisely on the real part of the first non-zero eigenvalue of the Lindblad equation, which determines the rate of approaching the stationary (ground) state.”
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“- Error correction: For OSDQSs, it is not guaranteed that error correction and fault-tolerant computing is possible in the sense defined above [134]”
What the sources say
- Not checked yetcites [134] source
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“If we can set the parameters of our AQS to a regime where efficient classical simulation is possible, we can assess the efficiency and reliability of the AQS in this case by direct comparison with classical simulations (see below).”
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In the paper
“Firm criteria on computational complexity and efficiency for AQSs are in general difficult to address and have not yet been established.”
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In the paper
“But, due to purely dissipative nature of the process, this type of simulation has a certain intrinsic robustness and built-in 'error correction.'”
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In the paper
“They found that decoherence and analog timing errors can make this inefficient for a Hamiltonian simulator.”
What the sources say
- Not checked yetcites [138] source
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In the paper
“One approach is by cross validation of a variety of different physical systems (e.g., atoms in optical lattices, ions in traps, and superconductors) [74].”
What the sources say
- Not checked yetcites [74] Dusuel S, 2004, J. Phys. A: Math. Gen. source
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In the paper
“Relying solely on validation from classical calculations, however, would restrict QSs to models in regimes where these efficient classical algorithms exist - that means contradicting our relevance and usefulness requirement, point (a) of our definition of a QS.”
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In the paper
“In these regimes, however, many relevant models become hypersensitive to perturbations [145, 146], and even small levels of noise may spoil completely the results of the quantum simulation.”
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In the paper
“Indeed, the capability of an analog quantum information processor whose dynamics is characterized by quantum chaos (i.e., well described by random matrix theory) can be severely impacted by imperfections [147, 148].”
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In the paper
“At zero temperature and disorder, the system undergoes a QPT when the dimensionless control parameter λ = h/J approaches the critical value, λ c = 1 , i.e., when the field intensity equals the interaction strength.”
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In the paper
“In particular, disorder can have a significant effect on relevant quantities that one could hope to extract from the simulator, such as critical points and exponents, or - if the system is described by a conformal field theory (CFT) - its central charge [177].”
What the sources say
- Not checked yetcites [177] source
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In the paper
“Without disorder and for infinite systems, ξ diverges at the critical point, because criticality is the emergence of collective phenomena involving infinite degrees of freedom at all length scales.”
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In the paper
“But, again due to the purely dissipative nature of the process, this type of simulation has a certain amount of intrinsic robustness and built-in 'error correction' - this is particularly clear for the OSAQS of quantum kinetic Ising models or Kitaev's toric code [173].”
What the sources say
- Not checked yetcites [173] source
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In the paper
“Nevertheless, in most of the proposals [126-128] or experimental realizations they allow for a wide control of parameters, which in turn allows for simulation of open-system (Markovian) evolutions for wide families of open systems.”
What the sources say
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In the paper
“This gives optimism that local quantities are robust enough to allow a faithful distinction between different quantum phases.”
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In the paper
“More importantly, this also means that successfully validating a QS in a classically accessible regime does not give certainty about its robustness in regimes which are classically not accessible.”
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In the paper
“- Error correction: For OSAQSs, it is not guaranteed that error correction and fault-tolerant computing is possible in the sense defined in the subsection on OSDQSs.”
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In the paper
“However, QSs have the advantage that we do not necessarily demand of the entire state to be robust. Often, it is enough if we can distinguish the relevant phases by measuring faithfully local observables (local in the quantum information sense that few sites are involved, although they may be physically far apart).”
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In the paper
“Due to this characteristic scaling of physical observables as a function of system size in pseudo-critical systems, criticality can be detected by studying a sequence of finite but increasingly large systems, a technique called finite-size scaling [186].”
What the sources say
- Not checked yetcites [186] source
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In the paper
“Because less-correlated quantum states can be described with fewer parameters, there is reason to suspect that certain aspects of weakly disordered quantum many-body systems could actually be easier to simulate on classical computers than their clean idealized versions.”
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In the paper
“At criticality, this entropy scales as c/ 6 log( L/π sin( lπ/L ))+ A [188-190].”
What the sources say
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In the paper
“Efficient classical algorithms for computing static properties of quantum systems are more developed than for computing dynamics (the difficulty arises mainly because entropy and correlations grow rapidly with simulated time).”
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In the paper
“Indeed, in a recent experiment based on ultracold bosonic atoms, the controlled dynamics ran for longer times than present classical algorithms based on matrix product states could efficiently track [14].”
What the sources say
- Not checked yetcites [14] source
plainSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“If the AQS can be operated below such a value, its results seem to be robust, at least in this simple model system.”
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In the paper
“Note also that the decrease of c with disorder indicates the destruction of correlations by disorder.”
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In the paper
“Therefore, if one simply neglects the influence of disorder, the extraction of critical exponents yields wrong results.”
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In the paper
“However, if the quench is global, it has been shown that the computational resources needed to keep a fixed amount of error grow exponentially with time [192, 193].”
What the sources say
- Not checked yetcites [192] source
- Not checked yetcites [193] Verstraete F Cirac J I, 2004
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In the paper
“Frequently, however, changing parameters from the regime where validation via classical simulation is possible to the regime of terra incognita might lead to uncontrolled disorder or noise.”
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In the paper
“This means that applying this analysis to a realworld AQS without correcting for disorder can yield erroneous results (compared to the ideal model) for the location of the QPT.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
- The authors state this as an assumption: The dynamical critical exponent ζ does not change much for small disorder.
None of the sources cited for this claim have been checked yet.
In the paper
“For systems with open boundary conditions, a fit to c/ 6 log( L/π sin( lπ/L ))+ A (excluding small values of l ) yields the effective central charge c [188-190].”
What the sources say
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Via a finite-size scaling, the gaps at finite systems also allows to extract the location of the QPT in the infinite system, as seen in Fig. A1.”
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In the paper
“Certainly, in some cases we believe it does, as for example in highT c superconductors [69] or in certain ground states of frustrated quantum antiferromagnets which are believed to carry topological order [89].”
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In the paper
“Indeed, as discussed above, a fault-tolerant implementation of the standard approach based on the Trotter expansion [98] comes at the cost of an overhead in the number of gates and time required that grows exponentially with the degree of precision required [64, 120].”
What the sources say
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In the paper
“The above discussion shows, however, that a digital implementation of a quantum simulation does not, in itself, guarantee an efficient and more powerful simulation than one that is carried out classically.”
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In the paper
“The transverse field Ising model, Eq. (1) of the main text, even with disorder, can be solved by casting it into the form of noninteracting fermionic particles using the Jordan-Wigner transformation,”
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In the paper
“Hence, using Eq. (A10) on a disordered AQS yields a too large critical exponent, compared to the ideal model.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
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
“Again, applying the analysis that is correct in the disorder-free case (where the system is indeed described by a conformal field theory) without adjustments to the disordered system, yields results which deviate from the desired ideal case.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
In the paper
“These cross at a series of pseudo-critical points which with increasing L tends rapidly to the critical point of the thermodynamic limit [202].”
What the sources say
- Not checked yetcites [202] Pineda C Barthel T Eisert J, 2009
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The disorder-free value is c = 0 . 5 .”
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- Probably not a substantial claim. 63
- It may state two separate claims as one. 52
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“Recently there has also been substantial progress in investigations of other possible candidates for AQS, such as photonic systems [31, 32, 34-36], photonic and polariton systems [33, 38-42], artificial lattices in solid state systems [44].”
What the sources say
- Partly supportedcites [31] sourceExperimental — accuracy not yet measured
The Abstract (page unavailable) reports a photonic implementation of Shor’s algorithm, supporting this paper as an example of progress with photonic quantum systems. It describes quantum computation, however, not photonic systems as candidates for AQS; the other platform categories in the citing sentence have separate citations. (LLM, conf=0.84)
- Partly supportedcites [32] sourceExperimental — accuracy not yet measured
The paper reports a photonic, all-optical implementation of a quantum-computing algorithm (pp. 1–2), supporting its use as an example of progress with photonic systems. It does not identify that experiment as analog quantum simulation or establish photonic systems as candidates for AQS. (LLM, conf=0.83)
- Supportedcites [34] source
The paper describes an experimental photonic analogue: ultrashort laser pulses create an analogue event horizon, and the authors report spontaneous photon emission (p. 1). It therefore supports the citation's photonic-systems example of progress in investigating candidates for analogue quantum simulation; it is not evidence for the separately cited polariton or solid-state examples. (LLM, conf=0.87)
- Not checked yetcites [35] Kitagawa T Broome M Fedrizzi A Rudner M Berg E Kassal I Aspuru -Guzik A Demler E White A G, 2011
- Supportedcites [36] source
The citation is attached to “photonic systems,” not to the separate claims about polariton systems or solid-state lattices. In “Quantum monogamy and complementarity” (p. 6), the paper describes its all-optical analog quantum simulator and reports generating and characterizing photonic states, making it an example of progress in photonic quantum simulation. (LLM, conf=0.93)
- Not checked yetcites [33] source
- Supportedcites [38] source
The opening passage (p. 1) introduces an array of coupled optical cavities whose interacting photon–atom states are polaritons, and predicts a quantum phase transition. The Conclusions (p. 3) describe the system as a potential tunable quantum simulator. This supports citing the paper as an example of progress on photonic and polaritonic candidates; the artificial-lattice example has its own citation. (LLM, conf=0.91)
- Supportedcites [39] source
The citation is attached to the photonic-and-polariton-systems category, not the separate artificial-lattices category. The opening passage (p. 1) proposes polaritons in cavity arrays as a quantum simulator, and the Introduction (p. 1) describes the system as an alternative way to simulate many-body Hamiltonians. (LLM, conf=0.91)
- Supportedcites [40] source
The Introduction (p. 1) proposes coupled electromagnetic cavities as an engineered quantum many-body system with polaritonic excitations. The conclusion (p. 4) says the arrays could simulate XY spin models, supporting their identification as a photonic or polaritonic candidate for analog quantum simulation. This citation need not support the sentence’s separate example of artificial solid-state lattices. (LLM, conf=0.90)
- Not checked yetcites [41] source
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.
- Partly supported
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show evidence that QSs appear to work better in regimes that are classically easier to solve or simulate (high-temperature states), thus hinting at a connection between the amount of quantum correlations and the robustness of a QS.”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — 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 Section VII, we show that the ground-state expectation values of certain local observables appear fairly robust under disorder, while this need not be true for the global many-body state of the simulator.”
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It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A: The correlation length ξ decreases with disorder r , and its peak broadens (shown for a chain of 400 spins).”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — 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 seen in Fig. 1B, the reduced simulator fidelities are much more robust to disorder than the global one - near the phase transition, f 2 ( r, λ ) decreases to approximately 0.998, and f 1 ( r, λ ) remains above 0.999.”
plaindirect- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — 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 Fig. 1A shows, however, disorder suppresses correlations and broadens the peak of ξ , thus making an extraction of the critical point much less reliable.”
plaindirect- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“C: The central charge c (full circles, left axis), extracted from a fit to the part-chain entropy, and the critical exponent ν (open circles, right axis), extracted from a collapse of the correlations in different chain lengths. Both change with disorder, which can lead to erroneously assigning the QPT to an incorrect universality class. However, the change begins relatively smoothly at low levels”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — 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 AQS keeps a high fidelity in the case of a local quench, while it performs poorly for the global quench, with fidelities reaching lows of 0 . 8 even for small systems of 50 spins.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.
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
“Disorder reduces the correlation length of the spin chain.”
plaindirect- 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
“Again, for low temperatures fidelity worsens, but saturates to a few percent. For high temperatures, it is simple to perform an expansion of the fidelity which shows that f 1 ≃ 1 -T -2 .”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- The authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.
In the paper
“As with the classical algorithms [192], the AQS remains faithful when the state is almost classical (high temperatures). The simulator fidelity decreases rapidly for low temperatures, although it saturates at a fairly high value.”
What the sources say
- Not checked yetcites [192] source
plaindirect- 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 authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Increasing disorder suppresses this, indicating the decrease of entanglement in the system (see Fig. 1C of the main text).”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
A result the paper reports from its own data — 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, the crossing point becomes less well defined with increasing disorder showing that this analysis should be corrected for the presence of disorder.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
- The authors state this as an assumption: The dynamical critical exponent ζ does not change much for small disorder.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finally, at large disorder, a second crossing point appears at lower λ . The two crossing points open up to a V-like structure with increasing disorder.”
plaindirect- 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.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
- The authors state this as an assumption: The dynamical critical exponent ζ does not change much for small disorder.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We can see how an analog quantum simulator works well when a classical solution is efficient, and worsens (but only in a limited way) when the problem becomes classically hard to simulate.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — 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 increasing disorder ( r = 0 . 2 , right), the collapse worsens, and the best collapse is obtained for some ν > 1 .”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“With increasing disorder ( r = 0 . 2 , right), the crossing point moves to larger values of λ and becomes less well defined. Also, at large disorder there appears a second crossing point below λ = 1 .”
hedgeddirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
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 such a situation, the error correction and fault tolerance are not guaranteed and the question of efficiency is even more pertinent.”
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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 specifically that little is known about reliability and efficiency of AQSs (question marks).”
plain- 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 may give no reason why it holds.
In the paper
“the tools to design, build, and implement QSs [1-3] have rapidly developed and are now reaching very sophisticated levels [4].”
What the sources say
- Not checked yetcites [4] source
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
“Measurements on this engineered machine, now known as a 'quantum simulator,' would reveal some unknown or difficult to compute properties of a model of interest.”
What the sources say
- Not checked yetcites [1] source
hedgeddirect- 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
“The requirements of reliability and efficiency are interrelated.”
plaincorrelational- 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 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
“modeling interesting physics associated with a quantum system involving 50 spin-1/2 particles - whose general description requires 2 50 ≈ 10 15 complex numbers - is out of the reach of current classical supercomputers, but perhaps within the grasp of a QS.”
hedged- 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
“In his seminal 1982 paper [1], Richard Feynman suggested that such models might be solved by 'simulation' with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics.”
What the sources say
- Not checked yetcites [1] source
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
“We argue that a useful quantum simulator must satisfy four conditions: relevance , controllability , reliability , and efficiency .”
plain- 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 may give no reason why it holds.
In the paper
“They found that for 100 spins, in order to achieve b ≥ 10 bits of precision, at least two levels of concatenated error correction are necessary, requiring at least 100 days of run time on the ion-trap quantum computer; for b ≥ 18 , three levels are necessary, requiring at least 7 . 5 × 10 3 years! These results assume a gate time of 10 µ s .”
What the sources say
- Not checked yetcites [120] source
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
“In fact, we could try to improve the precision of a QS by averaging more experiments, but in hypersensitive regimes (like close to quantum phase transitions) the necessary number of repetitions can grow rapidly, bringing the overall efficiency of the QS down to the level of classical computers.”
plaindirect- 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.
In the paper
“In particular, it is possible that for some classes of nUDQSs the problems of Trotterization are not as severe as in the case of UDQSs [101].”
What the sources say
- Not checked yetcites [101] source
hedged- 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
“In these cases, QMC works for various large systems, but fails for Fermi or frustrated systems due to the famous sign problem [75].”
What the sources say
- Not checked yetcites [75] source
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.
In the paper
“Moreover, Brown et al. showed that for a small number of qubits where one might avoid error correction, analog control errors on the logic gates can lead to faulty results, negating requirement (c), and robust control pulses become essential.”
What the sources say
- Not checked yetcites [64] source
plaindirect- 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.
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 nUDQSs, it is not guaranteed that error correction and fault-tolerant computing is possible.”
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.
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 may be, however, that the universal features shared by multiple platforms are robust only because they could have been predicted efficiently with some classical algorithm.”
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.
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 latter statement implies that while it might be possible to simulate with classical computers short-time dynamics in a restricted class of 1D models, such attempts will nearly always fail at longer time scales.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“Perturbation theory works only if there exists a small expansion parameter [76].”
What the sources say
- Not checked yetcites [76] Alba V, 2011, J. Stat. Mech.
plainconditional- 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.
None of the sources cited for this claim have been checked yet.
In the paper
“Mean field [85], DFT [86, 87], or DMFT [88], finally, have other limitations, e.g., they are essentially designed for weakly-correlated systems.”
What the sources say
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
“whereas 2D tensor-network methods (PEPS, MERA) in principle work for arbitrarily big systems (bosonic, and even fermionic [83] or frustrated [84]) but are biased towards slightly entangled states.”
What the sources say
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. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Generally speaking, computationally hard are those 'strongly entangled' models in more than 1D such as”
What the sources say
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
“Indeed, this fact is related to correlation and entanglement spreading according to the Lieb-Robinson theorem that states that, after a sufficiently large time, states can become strongly entangled ([91-96], see also [97]).”
What the sources say
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
“Exact diagonalization works only for rather small systems [75].”
What the sources say
- Not checked yetcites [75] source
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
“nUDQSs are typically not perfectly controllable, but in most experimental realizations should allow for a wide control of parameters, which in turn should allow for simulations of evolution for wide families of Hamiltonians of interest.”
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: 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.
None of the sources cited for this claim have been checked yet.
In the paper
“In the case of 1D systems, DMRG, MERA and TTN techniques scale favorably and can, in principle, treat very large systems [77-79].”
What the sources say
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.
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 non-universal AQSs such an addition requires additional resources.”
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: 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.
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
“- Error correction: UAQSs do not allow for standard error correction and fault tolerance.”
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.
In the paper
“The first step toward large-scale QSs with ions was, however, recently achieved [139].”
What the sources say
- Not checked yetcites [139] source
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
“For example, there may be models that have only one known implementation, or different implementations may suffer in the same way from imperfections, hence consistently exhibiting features associated with noise rather than with the ideal model.”
hedgedcorrelational- 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. 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
“- Error correction: AQSs do not allow for standard error correction and fault tolerance.”
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.
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
“All of these comments imply that in the area of OSDQSs there are more open questions than answers.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check 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. It may be too vague to check against evidence. 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 only difference is that UAQSs, by definition, are capable of performing tests of robustness of the quantum simulations that we propose in the following section, i.e., tests based on adding disorder or noise in a controlled manner to the simulated Hamiltonian.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check 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. 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
“While by definition they operate in continuous time and thus the Trotterization problems do not concern them, the standard error-correction methods and fault tolerance cannot be applied.”
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 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 by definition they operate in continuous time and thus the Trotterization problems do not concern them, the standard error-correction methods and fault tolerance cannot be applied.”
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.
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
“Most, if not all of the proposals for and realizations of AQSs allow for at least partial controllability.”
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.
None of the sources cited for this claim have been checked yet.
In the paper
“The most advanced experiments with AQSs have been with ultracold atoms in optical lattices [3, 5-15, 19, 71].”
What the sources say
- Not checked yetcites [3] Lewenstein M, 2012, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems source
- Not checked yetcites [5] source
- Not checked yetcites [6] source
- Not checked yetcites [7] source
- Not checked yetcites [8] source
- Not checked yetcites [9] source
- Not checked yetcites [10] source
- Not checked yetcites [11] source
- Not checked yetcites [12] source
- Not checked yetcites [13] source
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
“The degree of quantum control is even better in ultracold-ion systems, but these are so far limited to few ions [21-23, 26, 27].”
What the sources say
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 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
“At criticality, the low-energy spectrum of the Hamiltonian is gapless in the thermodynamic limit. In finite systems, it presents non-vanishing gaps that decrease in a systematic way with increasing system size.”
plaindirect- 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.
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
“Still, as in the case of OSDQSs, most of these general aspects concerning OSAQSs have not yet been investigated systematically.”
plain- 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
“Even more, in this Griffiths phase observables become non-selfaveraging, i.e., fluctuations increase with system size, and hence dominate the thermodynamic limit.”
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.
None of the sources cited for this claim have been checked yet.
In the paper
“The TIM, even under the presence of disorder, is efficiently solvable - by which we mean that the eigenstates and eigenenergies of the system can be found using a classical computer, and that the cost of the algorithms (in time and hardware) is polynomial with the size (number of particles) of the system.”
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
“In a universal quantum computation, the fidelity would have to be very close to 1 for the quantum computer to work fault-tolerantly.”
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.
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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
“The quantum Ising model, which we describe in detail in Section VI, is exactly solvable, which allows us to explore regions with universal behavior such as second-order QPTs.”
plaindirect- 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. 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, a state-of-the-art AQS can achieve very low levels of disorder, whence this is the experimentally relevant regime.”
plaindirect- 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. It may state two separate claims as one.
- The authors state this as an assumption: Considering small disorder strengths allows the Griffiths phase to be ignored, especially in finite-size systems.
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 practice, we can only deal with finite systems so that we cannot observe real criticality but only smoothed out signatures of it, a phenomenon which one normally calls 'pseudo-criticality.' For example, the correlation length ξ is bounded by the system size. Still, its peak gives a reliable signature for the location of the critical point.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“However, it is well known that even small disorder can lead to novel quantum phases such as Bose [182] or Fermi [183] glasses (see also the section on disorder in Ref. [184] and references therein).”
What the sources say
boosteddirect- Asserted: passes — The authors put it forward as true.
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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 what we have said, the rigorous answer to this question is 'no', yet in practice we do tend to trust them, at least to some extent.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Indeed, in the TIM when the disorder strength is comparable with the interactions, the critical point disappears and is replaced by a so called Griffiths phase [180], extending across a region of size proportional to the disorder strength.”
What the sources say
- Not checked yetcites [180] source
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The TIM, in particular, can be solved by using a Jordan-Wigner transformation to a system of non-interacting fermions - and the cost of solving the non-interacting fermion system is the cost of diagonalizing a matrix with rank equal to twice the number of spins in the chain [178].”
What the sources say
- Not checked yetcites [178] source
plaindirect- Asserted: passes — The authors put it forward as true.
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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
“OSAQSs are typically not universal in a sense similar to OSDQSs; they allow neither for simulating arbitrary (local) Markovian dynamics, nor do they allow for preparation of arbitrary states.”
hedged- Asserted: passes — The authors put it forward as true.
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In the paper
“All models within a given universality class give rise to the same collective behavior at large distances (typically large with respect to the lattice spacing), irrespective of their microscopic details [177]. Therefore, all relevant thermodynamic quantities for all models within a class are characterized by the same small set of critical exponents which describe the power-law decay of the”
What the sources say
- Not checked yetcites [177] source
plaindirect- Asserted: passes — The authors put it forward as true.
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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
“- Realizations: All AQS systems can, in principle, be used as OSAQSs.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“This model is well studied (see for instance [179]): for low fields, the ground state is a ferromagnet, while for large fields it is a paramagnet.”
What the sources say
- Not checked yetcites [179] source
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. It may state two separate claims as one.
In the paper
“If the QPT is described by a CFT (a specific subclass of one-dimensional critical systems), it is characterized by a central charge c . The central charge appears ubiquitously [187].”
What the sources say
- Not checked yetcites [187] source
plaincorrelational- 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
“We know that for noise above certain levels a digital quantum circuit is classically simulatable and for levels below a certain threshold it can be rendered fault tolerant.”
boosteddirect- 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. It may state two separate claims as one.
In the paper
“In the context of many-body physics, the success of DMRG in, e.g., 1D spin chains, is rigorously related to the existence of efficient matrix-product-state representations [197].”
What the sources say
- Not checked yetcites [197] source
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
“For example, models whose collective behavior is that of a free Majorana fermion (as in the disorder-free TIM) have central charge = 1 / 2 , while models whose collective behavior is that of a free boson have central charge = 1 .”
plaincorrelational- 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
“This suggests that such an AQS could perform well in a laboratory demonstration.”
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.
In the paper
“The effect of disorder in both the decay rate and the asymptotic saturation value can, in general, be understood from established techniques such as Fermi Golden's rule, and random matrices [191].”
What the sources say
- Not checked yetcites [191] source
plaindirect- Asserted: passes — The authors put it forward as true.
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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
“On the other hand, the effect of the initial state and the external driving is known to be nontrivial and of particular interest for our purposes.”
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“In higher-dimensional lattices, states which obey the socalled 'Area law' [97], where quantum correlations are smaller than in generic states, may still be amenable to a classical simulation using state-of-the-art techniques such as tensor networks [77, 81, 82, 198, 199], Density Functional Theories [86], or Quantum Monte Carlo [75].”
What the sources say
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“This happens, for example, in the realm of digital quantum computation, where a quantum circuit becomes classically simulatable for noise levels above a certain level when quantum gates lose their entangling power [194196].”
What the sources say
- Not checked yetcites [194196]
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Strictly speaking, the TIM has an underlying CFT only in the disorder-free case, but there have been efforts to extract an effective central charge also for the disordered model [181], for example, from the von Neumann entropy S of the reduced density matrix of a part of the chain of size l .”
What the sources say
- Not checked yetcites [181] Barber M N, 1983, Phase Transitions and Critical Phenomena
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
In the paper
“Using the same setup with a global quench, but starting from a thermal initial state, tDMRG becomes efficient for high temperatures [192] where the state and its correlations are almost classical. However, it becomes exponentially inefficient with time for low-temperature initial states.”
What the sources say
- Not checked yetcites [192] source
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
“In fact, in many experimental situations one hopes to reach levels of disorder or noise that are below a few percents, assuring the robustness of the AQS.”
plaindirect- 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
“Generically, solving for the dynamics of a quantum manybody system is a hard problem for classical algorithms.”
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
“Hence, ignoring the effects of disorder would give completely erroneous results, since even a small deviation of the central charge indicates a completely different universality class.”
boosteddirect- 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
“Our main discussion focused on AQSs, but similar issues pertain to DQSs.”
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
“The findings of both rows of figures mean that, ignoring the effects of disorder in an imperfect AQS yields, compared to the ideal model, too large values for the critical exponent as well as the location of the critical point.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.
- The authors state this as an assumption: The dynamical critical exponent ζ does not change much for small disorder.
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
“Away from criticality, the correlations decay as C ( i, j ) ∝ exp( -| i -j | /ξ ) with correlation length ξ .”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The correlations are intrinsically connected to the energy gap ∆( L ) , since a gapped system necessarily has exponentially decaying correlations [201].”
What the sources say
- Not checked yetcites [201] Sorella S Becca F 2011
plaindirect- Asserted: passes — The authors put it forward as true.
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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 a given model can be described by a conformal field theory, its universal critical behavior (including all critical exponents) is completely defined by a single number, the central charge c .”
plaindirect- 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.
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 initial state is not pure, but a thermal state, the state remains mixed even if the evolution is unitary. In this case, we cannot compute the fidelity for the full many-body state, but only the fidelity of the reduced density matrix for a few spins.”
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
“Without disorder, <!-- formula-not-decoded --> for some universal function f [177]. Hence, one can extract the critical exponent for the correlation length ν from a data collapse of the correlations.”
What the sources say
- Not checked yetcites [177] source
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
“For computing fidelities, we use the convenient Levitov's formula [204, 205], which relates traces of operators in the Hilbert space of the fermions to determinants of much smaller matrices (like H ).”
What the sources say
- Not checked yetcites [204] source
- Not checked yetcites [205] Shi Q Li S Zhao J Zhou H, 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.
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
“There, we plot curves 1 / ( L ζ ∆( L )) for closeby chain lengths L , where ζ is the dynamical critical exponent, which for the disorder-free case equals 1.”
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
“For the case of a single spin, the symmetry of the system ensures that at all times the reduced density matrix can be written as ρ = (1+ < σ i x > σ i x ) / 2 . Since < σ i x > = c † i c i , we only need to compute the evolution of the diagonal terms in the G correlation matrix.”
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. 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
“Even though the underlying model is actually solvable, this may be positive evidence for the existence of an intermediate regime of noise, and the efficiency of AQSs in more complex situations.”
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. 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
“As in any quantum algorithm, initialization, evolution of the state, and measurement must be performed efficiently, i.e., with a polynomial use of physical resources (space and time). Digital quantum simulation is no exception.”
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. It may state two separate claims as one.
The paper relies on this without support.
Various fundamental phenomena of strongly correlated quantum systems, such as high-Tc superconductivity, the fractional quantum-Hall effect, and quark confinement, are still awaiting a universally accepted explanation.
“Various fundamental phenomena of strongly-correlated quantum systems such as highT c superconductivity, the fractional quantum-Hall effect, and quark confinement are still awaiting a universally accepted explanation.”
The authors state this as an assumption.
Quenched disorder is the only possible imperfection considered in the study.
“We study how imperfections affect the results of a AQS simulating that model, where, for simplicity, we assume quenched disorder as the only possible imperfection.”
The authors state this as an assumption.
Considering small disorder strengths allows the Griffiths phase to be ignored, especially in finite-size systems.
“In this study, we consider small disorder strengths, which allows us to ignore the Griffiths phase, especially in finite-size systems.”
The authors state this as an assumption.
In the absence of disorder, a quantum simulation of dynamics can much more easily outperform classical computers.
“Therefore, one can assume that in the absence of disorder, a quantum simulation of dynamics can much more easily outperform classical computers.”
The paper relies on this without support.
There is no known way to fault-tolerantly error-correct analog quantum simulators.
“Since to date there exists no known way to fault-tolerantly error-correct AQSs, there is a natural tendency to explore the advantages of DQSs, where error correction is possible.”
The paper relies on this without support.
Real materials, such as high-Tc cuprates, have imperfections.
“For any real material, like a highT c cuprate, has imperfections.”
The authors state this as an assumption.
The dynamical critical exponent ζ does not change much for small disorder.
“Assuming that it does not change much for small disorder, we identify as an approximation the critical point with the mean of the crossing points curves 1 / ( L ∆( L )) for L = 100 , 150 , 200 , 300 , 350 , 400 with 10000 realizations of disorder each.”
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 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 [64]
Citations
Cites
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
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Hoch, M. J. R. (2016) · CRC Press eBooks · doi:10.1201/9781439850541-13 · Cited by 11,466
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
Simulating physics with computers
Feynman, R. P. (1982) · International Journal of Theoretical Physics · doi:10.1007/bf02650179 · Cited by 7,691
Georges, A., Kotliar, G., Krauth, W., & Rozenberg, M. J. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.13 · Cited by 6,901
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Quantum theory, the Church–Turing principle and the universal quantum computer
Deutsch, D. (1985) · Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences · doi:10.1098/rspa.1985.0070 · Cited by 4,597
Doping a Mott insulator: Physics of high-temperature superconductivity
Lee, P. A., Nagaosa, N., & Wen, X.-G. (2006) · Reviews of Modern Physics · doi:10.1103/revmodphys.78.17 · Cited by 4,582
Scheme for reducing decoherence in quantum computer memory
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Cited by
Sorted by citations
Georgescu, I. M., Ashhab, S., & Nori, F. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.153 · Cited by 2,932
“Disorder, noise and other imperfections might affect the reliability of the quantum simulation (Hauke et al., 2012).”
BackgroundQuantum many-body systems out of equilibrium
Eisert, J., Friesdorf, M., & Gogolin, C. (2015) · Nature Physics · doi:10.1038/nphys3215 · Cited by 1,255
Programmable quantum simulations of spin systems with trapped ions
Monroe, C. R., Campbell, W. C., Duan, L.-M., Gong, Z., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N. M., Pagano, G., et al. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.025001 · Cited by 891
“Further, simulations with systems that lack universal gate sets or the digital simulation of open systems may render faulttolerance unavailable in a DQS (Hauke et al., 2012).”
Programmable Quantum Simulations of Spin Systems with Trapped Ions
Monroe, C., Campbell, W. C., Duan, L. M., Gong, Z. X., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N., Pagano, G., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.07845 · Cited by 806
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges
Saffman, M. E. (2016) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/49/20/202001 · Cited by 740
Metadata
- Authors
- Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M.
- Affiliations
- Institute of Photonic Sciences (ES)
- University of New Mexico (US)
- Institució Catalana de Recerca i Estudis Avançats (ES)
- Corresponding author
- Hauke, Philipp
- Venue
- Reports on Progress in Physics
- Publisher
- IOP Publishing
- Published
- 2012-07-24
- Volume
- 75
- Issue
- 8
- Pages
- 082401
- ISSN
- 0034-4885 (ISSN-L)
- 1361-6633
- OpenAlex
- W2093995600
- Cited by
- 315
- References
- 205
- Citations by year
- 2026: 3 · 2025: 18 · 2024: 13 · 2023: 15 · 2022: 25 · 2021: 29 · 2020: 19 · 2019: 50 · 2018: 20 · 2017: 15 · 2016: 15 · 2015: 20 · 2014: 32 · 2013: 23 · 2012: 17
- FWCI
- 15.15
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reports on Progress in Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Institutional Research Information System (Università degli Studi di Trento) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- quantum simulators, transverse-field Ising model, analog quantum simulation, digital quantum simulation, controllability, strongly correlated systems, high-temperature superconductivity, fractional quantum Hall effect, quark confinement
- MeSH terms
- Algorithms, Computer Simulation, Models, Chemical, Numerical Analysis, Computer-Assisted, Quantum Theory
About these checks
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.
A language model drew the claims from the paper on 2026-10-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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