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Cited by 315Quantum many-body systemsQuantum Computing Algorithms and ArchitectureCold Atom Physics and Bose-Einstein Condensates

Can one trust quantum simulators?

Open access
Hauke, Philipp, Cucchietti, Fernando M, Tagliacozzo, Luca, Deutsch, Ivan, Lewenstein, Maciej·2012·Reports on Progress in Physics
DOI 10.1088/0034-4885/75/8/082401
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Abstract

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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Written from the paper’s full text.

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.

Model-written summary. Check it against the paper before relying on it.

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Crossref · 10.1088/0034-4885/75/8/082401

Cites

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Claims the paper makes

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  • Findingown data
    § Can One Trust Quantum Simulators? · p. 1

    Disorder can decrease the reliability of an analog quantum simulator of 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”
    Quote in the paperSubstantial claim
  • Findingown data
    § Can One Trust Quantum Simulators? · p. 1

    Large errors in local observables are introduced only for strong levels of disorder.

    “although large errors in local observables are introduced only for strong levels of disorder.”
    Quote in the paperSubstantial claim
  • Findingown data
    § VII. RESULTS - STATICS · p. 11

    If one does not correct for disorder effects, one would locate the critical point at values of λ that are too large.

    “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.”
    Quote in the paperSubstantial claim
  • Findingown data
    § VII. RESULTS - STATICS · p. 11

    The simulator fidelity overlap is considerably suppressed near the QPT, reaching values as low as 55% for r = 0.1 in a chain of L = 400 sites.

    “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).”
    Quote in the paperSubstantial claim
  • Findingown data
    § VI. THE MODEL · p. 11

    For a chain of 400 spins at fixed disorder level r = 0.1, local fidelities are more robust than the total simulator fidelity.

    “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.”
    Quote in the paperSubstantial claim
  • May combine two claims. 52
  • Classified as probably not a substantial claim. 63

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    Findingown data
    § V. ROBUSTNESS OF ANALOG QUANTUM SIMULATORS · p. 10

    QSs appear to work better in regimes that are classically easier to solve or simulate (high-temperature states), hinting at a connection between the amount of quantum correlations and the robustness of a QS.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § V. ROBUSTNESS OF ANALOG QUANTUM SIMULATORS · p. 10

    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.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § VI. THE MODEL · p. 11

    The correlation length ξ decreases with disorder r, and its peak broadens (shown for a chain of 400 spins).

    “A: The correlation length ξ decreases with disorder r , and its peak broadens (shown for a chain of 400 spins).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data
    § VII. RESULTS - STATICS · p. 11

    The reduced simulator fidelities are much more robust to disorder than the global one; near the phase transition, f2 decreases to approximately 0.998, and f1 remains above 0.999.

    “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.”
    Quote in the paperSubstantial claim

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    Findingown data
    § VII. RESULTS - STATICS · p. 11

    Disorder suppresses correlations and broadens the peak of ξ, making extraction of the critical point much less reliable.

    “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.”
    Quote in the paperSubstantial claim

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    Findingown data
    § VI. THE MODEL · p. 11

    The central charge c and critical exponent ν both change with disorder, which can lead to erroneously assigning the QPT to an incorrect universality class; the change begins relatively smoothly at low levels of disorder.

    “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”
    Quote in the paperSubstantial claim

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    Findingown data
    § VIII. RESULTS - DYNAMICS · p. 12

    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.

    “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.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.

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

    Findingnone given
    § IX. DISCUSSION AND OUTLOOK · p. 13

    Disorder reduces the correlation length of the spin chain.

    “Disorder reduces the correlation length of the spin chain.”
    Quote in the paperNot a substantial claim

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    Findingreasoning
    § VIII. RESULTS - DYNAMICS · p. 13

    For low temperatures, fidelity worsens, but saturates to a few percent; for high temperatures, f1 ≃ 1 - T^-2.

    “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 .”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Quenched disorder is the only possible imperfection considered in the study.

  • May combine two claims.

    Findingown data
    § VIII. RESULTS - DYNAMICS · p. 13

    As with classical algorithms, 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.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [192] source

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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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    Findingown data
    § Appendix · p. 15

    Increasing disorder suppresses the effective central charge, indicating a decrease of entanglement in the system.

    “Increasing disorder suppresses this, indicating the decrease of entanglement in the system (see Fig. 1C of the main text).”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.

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    Findingown data
    § Appendix · p. 15

    The crossing point becomes less well defined with increasing disorder, showing that the analysis should be corrected for the presence of disorder.

    “Moreover, the crossing point becomes less well defined with increasing disorder showing that this analysis should be corrected for the presence of disorder.”
    Quote in the paperSubstantial claim
    • 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.

  • May combine two claims.

    Findingown data
    § Appendix · p. 15

    At large disorder, a second crossing point appears at lower λ, and the two crossing points open up to a V-like structure with increasing disorder.

    “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.”
    Quote in the paperNot a substantial claim
    • 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.

  • May combine two claims.

    Findingown data
    § IX. DISCUSSION AND OUTLOOK · p. 14

    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.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Appendix · p. 16

    For increasing disorder (r=0.2), the collapse worsens, and the best collapse is obtained for some ν > 1.

    “For increasing disorder ( r = 0 . 2 , right), the collapse worsens, and the best collapse is obtained for some ν > 1 .”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.

  • May combine two claims.

    Findingown data
    § Appendix · p. 16

    With increasing disorder (r=0.2), the crossing point moves to larger values of λ and becomes less well defined; at large disorder a second crossing point appears below λ=1.

    “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 .”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Real materials, such as high-Tc cuprates, have imperfections.

  • May combine two claims.

    Interpretationreasoning
    § I. INTRODUCTION · p. 2

    For digital quantum simulators with only a limited, non-universal set of gates, error correction and fault tolerance are not guaranteed and the question of efficiency is even more pertinent.

    “In such a situation, the error correction and fault tolerance are not guaranteed and the question of efficiency is even more pertinent.”
    Quote in the paperSubstantial claim

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

    Premisenone given
    § Definition · p. 3

    Little is known about the reliability and efficiency of analog quantum simulators.

    “Note specifically that little is known about reliability and efficiency of AQSs (question marks).”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § I. INTRODUCTION · p. 1

    The tools to design, build, and implement quantum simulators have rapidly developed and are now reaching very sophisticated levels.

    “the tools to design, build, and implement QSs [1-3] have rapidly developed and are now reaching very sophisticated levels [4].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
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    Premisecitation
    § Can One Trust Quantum Simulators? · p. 1

    Measurements on an engineered quantum simulator would reveal unknown or difficult-to-compute properties of a model of interest.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] source

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    Interpretationreasoning
    § Definition · p. 4

    The requirements of reliability and efficiency are interrelated.

    “The requirements of reliability and efficiency are interrelated.”
    Quote in the paperNot a substantial claim

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

    Premisereasoning
    § I. INTRODUCTION · p. 1

    Modeling 50 spin-1/2 particles requires about 2^50 complex numbers, which is out of reach of current classical supercomputers but perhaps within the grasp of a quantum simulator.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisecitation
    § Can One Trust Quantum Simulators? · p. 1

    Feynman suggested that quantum many-body models might be solved by simulation with a new type of computer whose constituent parts are governed by a desired quantum many-body dynamics.

    “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.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1] source

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

    Interpretationnone given
    § Can One Trust Quantum Simulators? · p. 1

    A useful quantum simulator must satisfy four conditions: relevance, controllability, reliability, and efficiency.

    “We argue that a useful quantum simulator must satisfy four conditions: relevance , controllability , reliability , and efficiency .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § A. Universal Digital Quantum Simulators (UDQS) · p. 6

    Clark et al. found that for 100 spins, achieving at least 10 bits of precision requires at least two levels of concatenated error correction and at least 100 days of run time, while achieving at least 18 bits requires three levels and at least 7.5×10^3 years, assuming a gate time of 10 microseconds.

    “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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [120] source

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    Interpretationnone given
    § Definition · p. 4

    In hypersensitive regimes, the number of repetitions needed to improve precision can grow rapidly, bringing the overall efficiency of a quantum simulator down to the level of classical computers.

    “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.”
    Quote in the paperNot a substantial claim

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

    Interpretationcitation
    § B. Non-Universal Digital Quantum Simulators (nUDQS) · p. 6

    It is possible that for some classes of non-universal digital quantum simulators the problems of Trotterization are not as severe as in the case of universal digital quantum simulators.

    “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].”
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    • cites [101] source

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    Premisecitation
    § Definition · p. 4

    Quantum Monte Carlo works for various large systems but fails for Fermi or frustrated systems due to the sign problem.

    “In these cases, QMC works for various large systems, but fails for Fermi or frustrated systems due to the famous sign problem [75].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [75] source

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    Premisecitation
    § A. Universal Digital Quantum Simulators (UDQS) · p. 6

    Brown et al. showed that for a small number of qubits where one might avoid error correction, analog control errors on logic gates can lead to faulty results, negating the reliability requirement, and robust control pulses become essential.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [64] source

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    Interpretationnone given
    § B. Non-Universal Digital Quantum Simulators (nUDQS) · p. 6

    For non-universal digital quantum simulators, error correction and fault-tolerant computing are not guaranteed.

    “For nUDQSs, it is not guaranteed that error correction and fault-tolerant computing is possible.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given
    § Definition · p. 4

    Universal features shared by multiple platforms in cross-validation may be robust only because they could have been predicted efficiently with some classical algorithm.

    “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.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Definition · p. 4

    While short-time dynamics in a restricted class of one-dimensional models might be simulated classically, such attempts will nearly always fail at longer time scales.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisecitation
    § Definition · p. 4

    Perturbation theory works only if there exists a small expansion parameter.

    “Perturbation theory works only if there exists a small expansion parameter [76].”
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    • cites [76] Alba V, 2011, J. Stat. Mech.

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    Premisecitation
    § Definition · p. 4

    Mean field, DFT, and DMFT have limitations, for example they are essentially designed for weakly correlated systems.

    “Mean field [85], DFT [86, 87], or DMFT [88], finally, have other limitations, e.g., they are essentially designed for weakly-correlated systems.”
    Quote in the paperNot a substantial claim0 of 4 sources checked
    • cites [85] Stoudenmire E Wagner L O White S R Burke K, 2011

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    • cites [87] Misguich G, 2004, Frustrated Spin Systems

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    Premisecitation
    § Definition · p. 4

    Two-dimensional tensor-network methods such as PEPS and MERA in principle work for arbitrarily big systems but are biased towards slightly entangled states.

    “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.”
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    • cites [83] Binney J J, 1992, The Theory Of Critical Phenomena : an Introduction to the Renormalization Group source

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    • cites [84] source

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    Premisecitation
    § Definition · p. 4

    Strongly entangled models in more than one dimension are computationally hard, with examples including fermionic models, frustrated models, and disordered models.

    “Generally speaking, computationally hard are those 'strongly entangled' models in more than 1D such as”
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    • cites [68] Lee P A, 2008, Rep. Prog. Phys.

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    § Definition · p. 4

    According to the Lieb-Robinson theorem, after a sufficiently large time, states can become strongly entangled.

    “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]).”
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    • cites [91] source

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    • cites [94] Schuch N, 2008, New J. Phys. source

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    § Definition · p. 4

    Exact diagonalization works only for rather small systems.

    “Exact diagonalization works only for rather small systems [75].”
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    • cites [75] source

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

    Interpretationnone given
    § B. Non-Universal Digital Quantum Simulators (nUDQS) · p. 6

    Non-universal digital quantum simulators are typically not perfectly controllable, but in most experimental realizations they should allow wide control of parameters, allowing simulations of evolution for wide families of Hamiltonians of interest.

    “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.”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § Definition · p. 4

    In one-dimensional systems, DMRG, MERA and TTN techniques scale favorably and can in principle treat very large systems.

    “In the case of 1D systems, DMRG, MERA and TTN techniques scale favorably and can, in principle, treat very large systems [77-79].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [77] Evenbly G Vidal G, 2011

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    • cites [78] source

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    Interpretationnone given
    § A. Universal Analog Quantum Simulators (UAQS) · p. 8

    For non-universal AQSs, adding disorder or noise in a controlled manner requires additional resources.

    “For non-universal AQSs such an addition requires additional resources.”
    Quote in the paperNot a substantial claim

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    Premisenone given
    § A. Universal Analog Quantum Simulators (UAQS) · p. 8

    UAQSs do not allow for standard error correction and fault tolerance.

    “- Error correction: UAQSs do not allow for standard error correction and fault tolerance.”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    The first step toward large-scale QSs with ions was recently achieved.

    “The first step toward large-scale QSs with ions was, however, recently achieved [139].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [139] source

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    Interpretationreasoning
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 9

    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.

    “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.”
    Quote in the paperNot a substantial claim

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

    Premisenone given
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    AQSs do not allow for standard error correction and fault tolerance.

    “- Error correction: AQSs do not allow for standard error correction and fault tolerance.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning
    § C. Open-System Digital Quantum Simulators (OSDQS) · p. 7

    In the area of open-system digital quantum simulators there are more open questions than answers.

    “All of these comments imply that in the area of OSDQSs there are more open questions than answers.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given
    § A. Universal Analog Quantum Simulators (UAQS) · p. 8

    UAQSs, by definition, are capable of performing tests of robustness based on adding disorder or noise in a controlled manner to the simulated Hamiltonian.

    “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.”
    Quote in the paperNot a substantial claim

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

    Premisereasoning
    § IV. ANALOG QUANTUM SIMULATORS (AQS) · p. 7

    Standard error-correction methods and fault tolerance cannot be applied to AQSs.

    “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.”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    Recently there has been substantial progress in investigations of other possible candidates for AQS, such as photonic systems, photonic and polariton systems, and artificial lattices in solid state systems.

    “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].”
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    • cites [31] source

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    • cites [34] source

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    • cites [35] Kitagawa T Broome M Fedrizzi A Rudner M Berg E Kassal I Aspuru -Guzik A Demler E White A G, 2011

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    • cites [41] source

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    Premisereasoning
    § IV. ANALOG QUANTUM SIMULATORS (AQS) · p. 7

    AQSs operate in continuous time, so Trotterization problems do not concern them.

    “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.”
    Quote in the paperNot a substantial claim

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    Premisenone given
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    Most, if not all, proposals for and realizations of AQSs allow for at least partial controllability.

    “Most, if not all of the proposals for and realizations of AQSs allow for at least partial controllability.”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    The most advanced experiments with AQSs have been with ultracold atoms in optical lattices.

    “The most advanced experiments with AQSs have been with ultracold atoms in optical lattices [3, 5-15, 19, 71].”
    Quote in the paperNot a substantial claim0 of 10 sources checked
    • cites [3] Lewenstein M, 2012, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems source

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    • cites [5] source

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    • cites [6] source

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    • cites [7] source

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    • cites [9] source

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    • cites [10] source

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    • cites [11] source

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    • cites [12] source

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    • cites [13] source

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    Premisecitation
    § B. Non-Universal Analog Quantum Simulators (nUAQS), or simply AQS · p. 8

    The degree of quantum control is even better in ultracold-ion systems, but these are so far limited to few ions.

    “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].”
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    • cites [21] source

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    • cites [23] source

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    • cites [26] source

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    • cites [27] source

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    Premisenone given
    § VII. RESULTS - STATICS · p. 11

    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 systematically with increasing system size.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisenone given
    § C. Open-System Analog Quantum Simulators (OSAQS) · p. 9

    Most general aspects concerning OSAQSs have not yet been investigated systematically.

    “Still, as in the case of OSDQSs, most of these general aspects concerning OSAQSs have not yet been investigated systematically.”
    Quote in the paperNot a substantial claim

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

    Premisenone given
    § VI. THE MODEL · p. 10

    In the Griffiths phase, observables become non-self-averaging, i.e., fluctuations increase with system size and dominate the thermodynamic limit.

    “Even more, in this Griffiths phase observables become non-selfaveraging, i.e., fluctuations increase with system size, and hence dominate the thermodynamic limit.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § VI. THE MODEL · p. 10

    The transverse Ising model (TIM), even under disorder, is efficiently solvable: its eigenstates and eigenenergies can be found using a classical computer, and the cost of the algorithms is polynomial with system size.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisenone given
    § VII. RESULTS - STATICS · p. 11

    In a universal quantum computation, the fidelity would have to be very close to 1 for the quantum computer to work fault-tolerantly.

    “In a universal quantum computation, the fidelity would have to be very close to 1 for the quantum computer to work fault-tolerantly.”
    Quote in the paperNot a substantial claim

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

    Premisenone given
    § V. ROBUSTNESS OF ANALOG QUANTUM SIMULATORS · p. 10

    The quantum Ising model is exactly solvable, which allows exploration of regions with universal behavior such as second-order QPTs.

    “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.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given
    § VI. THE MODEL · p. 10

    State-of-the-art AQS can achieve very low levels of disorder, so small disorder is the experimentally relevant regime.

    “Moreover, a state-of-the-art AQS can achieve very low levels of disorder, whence this is the experimentally relevant regime.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Considering small disorder strengths allows the Griffiths phase to be ignored, especially in finite-size systems.

  • May combine two claims.

    Premisereasoning
    § VII. RESULTS - STATICS · p. 11

    In practice, finite systems cannot exhibit real criticality but only smoothed out signatures (pseudo-criticality); the correlation length ξ is bounded by the system size, but its peak gives a reliable signature for the location of the critical point.

    “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.”
    Quote in the paperSubstantial claim

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    Premisecitation
    § VI. THE MODEL · p. 10

    It is well known that even small disorder can lead to novel quantum phases such as Bose or Fermi glasses.

    “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).”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [182] Cardy J, 2010

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    • cites [183] source

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    • cites [184] source

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

    Interpretationreasoning
    § V. ROBUSTNESS OF ANALOG QUANTUM SIMULATORS · p. 10

    The rigorous answer to whether we can trust quantum simulators is 'no', yet in practice we do tend to trust them, at least to some extent.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § VI. THE MODEL · p. 10

    In the TIM, when disorder strength is comparable with the interactions, the critical point disappears and is replaced by a Griffiths phase extending across a region of size proportional to the disorder strength.

    “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.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [180] source

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    Premisecitation
    § VI. THE MODEL · p. 10

    The TIM 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.

    “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].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [178] source

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  • May combine two claims.

    Premisenone given
    § C. Open-System Analog Quantum Simulators (OSAQS) · p. 9

    OSAQSs are typically not universal in a sense similar to OSDQSs; they allow neither for simulating arbitrary (local) Markovian dynamics, nor for preparation of arbitrary states.

    “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.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § VII. RESULTS - STATICS · p. 12

    All models within a given universality class give rise to the same collective behavior at large distances, irrespective of microscopic details, and are characterized by the same critical exponents.

    “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”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [177] source

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    Premisenone given
    § C. Open-System Analog Quantum Simulators (OSAQS) · p. 9

    All AQS systems can, in principle, be used as OSAQSs.

    “- Realizations: All AQS systems can, in principle, be used as OSAQSs.”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § VI. THE MODEL · p. 10

    For the TIM, for low fields the ground state is a ferromagnet, while for large fields it is a paramagnet.

    “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.”
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    • cites [179] source

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    Premisecitation
    § VII. RESULTS - STATICS · p. 12

    If the QPT is described by a CFT, it is characterized by a central charge c.

    “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].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [187] source

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    Premisenone given
    § IX. DISCUSSION AND OUTLOOK · p. 14

    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.

    “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.”
    Quote in the paperNot a substantial claim

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    Premisecitation
    § IX. DISCUSSION AND OUTLOOK · p. 13

    In many-body physics, the success of DMRG in 1D spin chains is rigorously related to the existence of efficient matrix-product-state representations.

    “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].”
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    • cites [197] source

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

    Premisenone given
    § VII. RESULTS - STATICS · p. 12

    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.

    “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 .”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning
    § IX. DISCUSSION AND OUTLOOK · p. 13

    Such an AQS could perform well in a laboratory demonstration.

    “This suggests that such an AQS could perform well in a laboratory demonstration.”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § VIII. RESULTS - DYNAMICS · p. 12

    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.

    “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].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [191] source

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    Premisenone given
    § VIII. RESULTS - DYNAMICS · p. 12

    The effect of the initial state and the external driving is known to be nontrivial and of particular interest.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisecitation
    § IX. DISCUSSION AND OUTLOOK · p. 14

    In higher-dimensional lattices, states obeying the Area law may still be amenable to classical simulation using tensor networks, density functional theories, or quantum Monte Carlo.

    “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].”
    Quote in the paperNot a substantial claim0 of 7 sources checked
    • cites [97] source

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    • cites [77] Evenbly G Vidal G, 2011

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    • cites [81] source

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    • cites [82] Wang L Gu Z Wen X Verstraete F, 2011

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    • cites [198] source

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    Premisecitation
    § IX. DISCUSSION AND OUTLOOK · p. 13

    In digital quantum computation, a quantum circuit becomes classically simulatable for noise levels above a certain level when quantum gates lose their entangling power.

    “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].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [194196]

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    Premisecitation
    § VII. RESULTS - STATICS · p. 12

    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.

    “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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [181] Barber M N, 1983, Phase Transitions and Critical Phenomena

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  • May combine two claims.

    Premisecitation
    § VIII. RESULTS - DYNAMICS · p. 13

    Using a global quench but starting from a thermal initial state, tDMRG becomes efficient for high temperatures, but becomes exponentially inefficient with time for low-temperature initial states.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [192] source

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    Interpretationnone given
    § VII. RESULTS - STATICS · p. 12

    In many experimental situations one hopes to reach levels of disorder or noise below a few percents, assuring the robustness of the AQS.

    “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.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisenone given
    § VIII. RESULTS - DYNAMICS · p. 12

    Generically, solving for the dynamics of a quantum many-body system is a hard problem for classical algorithms.

    “Generically, solving for the dynamics of a quantum manybody system is a hard problem for classical algorithms.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § VII. RESULTS - STATICS · p. 12

    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.

    “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.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning
    § IX. DISCUSSION AND OUTLOOK · p. 14

    Similar issues to those discussed for analog quantum simulators pertain to digital quantum simulators.

    “Our main discussion focused on AQSs, but similar issues pertain to DQSs.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data
    § Appendix · p. 16

    Ignoring the effects of disorder in an imperfect analog quantum simulator yields, compared to the ideal model, too large values for the critical exponent as well as the location of the critical point.

    “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.”
    Quote in the paperSubstantial claim
    • 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.

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

    Premisenone given
    § Appendix · p. 15

    Away from criticality, the correlations decay exponentially with distance, C(i,j) ∝ exp(-|i-j|/ξ), with correlation length ξ.

    “Away from criticality, the correlations decay as C ( i, j ) ∝ exp( -| i -j | /ξ ) with correlation length ξ .”
    Quote in the paperNot a substantial claim

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

    Premisecitation
    § Appendix · p. 15

    A gapped system necessarily has exponentially decaying correlations.

    “The correlations are intrinsically connected to the energy gap ∆( L ) , since a gapped system necessarily has exponentially decaying correlations [201].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [201] Sorella S Becca F 2011

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

    Premisenone given
    § Appendix · p. 15

    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.

    “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 .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § Appendix · p. 16

    If the initial state is not pure but a thermal state, the state remains mixed even if the evolution is unitary, so the fidelity of the full many-body state cannot be computed; only the fidelity of the reduced density matrix for a few spins can be computed.

    “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.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § Appendix · p. 15

    Without disorder, the correlation length scaling follows a universal function f, allowing extraction of the critical exponent ν from a data collapse of the correlations.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [177] source

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    Premisecitation
    § Appendix · p. 16

    Levitov's formula relates traces of operators in the fermionic Hilbert space to determinants of much smaller matrices.

    “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 ).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [204] source

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    • cites [205] Shi Q Li S Zhao J Zhou H, 2009

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    Premisenone given
    § Appendix · p. 15

    For the disorder-free case, the dynamical critical exponent ζ equals 1.

    “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.”
    Quote in the paperSubstantial claim

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

    Premisereasoning
    § Appendix · p. 16

    For 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, and since <σ_i^x> = c_i† c_i, only the evolution of the diagonal terms in the G correlation matrix needs to be computed.

    “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+ &lt; σ i x &gt; σ i x ) / 2 . Since &lt; σ i x &gt; = c † i c i , we only need to compute the evolution of the diagonal terms in the G correlation matrix.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationown data
    § IX. DISCUSSION AND OUTLOOK · p. 14

    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.

    “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.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given
    § IX. DISCUSSION AND OUTLOOK · p. 14

    In any quantum algorithm, initialization, evolution of the state, and measurement must be performed efficiently, with polynomial use of physical resources (space and time); digital quantum simulation is no exception.

    “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.”
    Quote in the paperNot a substantial claim
95 of 95

  • 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.”
7 of 7

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?

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. Lee P A, 2008, Rep. Prog. Phys., 71
  2. Alba V, 2011, J. Stat. Mech.
  3. Aharonov D Ta-Shma A, 2003, Proc. 35th STOC, 20
  4. Calabrese P, 2004, J. Stat. Mech., 2004

Cited by

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Related

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
ORCID
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
DOI
10.1088/0034-4885/75/8/082401
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
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.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.

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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