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Cited by 127Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Mechanics and Applications

What is a quantum simulator?

Open access
Johnson, Tomi H, Clark, Stephen R, Jaksch, Dieter·2014·EPJ Quantum Technology
DOI 10.1140/epjqt10
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Abstract

Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. In this review we expand on this definition by answering several fundamental questions about the nature and use of quantum simulators. Our answers address two important areas. First, the difference between an operation termed simulation and another termed computation. This distinction is related to the purpose of an operation, as well as our confidence in and expectation of its accuracy. Second, the threshold between quantum and classical simulations. Throughout, we provide a perspective on the achievements and directions of the field of quantum simulation. PACS Codes: 03.65.-w, 03.67.Ac, 03.67.Lx.

AI snapshot

Written from the paper’s full text.

TL;DR

This review argues that a quantum simulator is a device whose simulating degrees of freedom behave non-classically during operation, and that simulators differ from computers by purpose and guaranteed accuracy. It surveys when quantum simulators are needed and how trust in them can be built through falsifiable tests rather than full verification.

Key findings

  • Simulator vs. computer: a simulator reveals information about a model and is typically compared to a real system, while a computer has arbitrarily controllable and guaranteed accuracy, allowing interpretation without reference to a real system. The authors classify Lloyd’s digital quantum simulator as effectively a universal quantum computer and agree with calling D-Wave’s Ising ground-state device a computer.
  • Quantum/classical boundary: a device is classical if its relevant density operator is diagonal in some single-particle basis at all times; it is quantum if not, e.g. through entanglement between modes. Examples: room-temperature semiconductor computing is classical; classical annealing is classical; quantum annealing is expected to be quantum; a single-mode Bose-Einstein condensate/Gross-Pitaevskii description is classical; a Gibbons-Hawking effect simulator is quantum.
  • Need for quantum simulators: Feynman in 1982 noted that classically calculating properties of an arbitrary quantum model scales exponentially with particle number, while a quantum device might scale at most polynomially. Classical methods have limits: exact calculations only for small Hilbert spaces, mean-field only for weak correlations, tensor networks often fail with strong entanglement, DFT struggles with strong correlations, and quantum Monte Carlo suffers the sign problem; finding the ground state of even a classical Ising model is NP-hard.
  • Trustworthiness: tests can falsify but not verify a simulator; a simulator could pass tests yet have significant errors, and confidence is not objective but changes over time. The authors argue simulators should be falsifiable like models, and analogue quantum simulators are the most easily scaled and likely near-term.

Methods

  • Design: conceptual review/perspective, not an empirical study; no data or sample are reported.
  • Analysis: defines and classifies simulators vs. computers and quantum vs. classical devices, then discusses how simulators are used, why quantum simulators are needed, when they are trustworthy, and future directions.
  • Evidence base: arguments and examples drawn from prior literature across trapped ions, cold atoms, NMR, photons, quantum dots, superconducting circuits, and NV centres; no statistical or experimental analysis is performed.

Limitations

  • Paper states: the chosen boundary between quantum and classical is one of many possibilities, and defining the quantumness of a simulation entirely by the device is not common.
  • Paper states: there is no guarantee that a classical device or algorithm will not sometime in the future efficiently study some subset of the quantum models discussed; tests cannot verify accuracy and may miss similar or correlated errors.
  • Evident: as a review/opinion piece, it presents the authors’ conceptual positions without a systematic review protocol or new empirical data, so its definitions and trust framework are not tested here.

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

Integrity signals

Registry

Crossref · 10.1140/epjqt10

Cites

129 of 129 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 5 cited sources checked · 0 supported · 0 flagged

  • Interpretationreasoning

    The paper's condition of classicality ensures there is always a single-particle basis in which dephasing would have no effect.

    “This condition ensures there is always a single-particle basis in which dephasing would have no effect.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning

    The paper's condition of classicality disallows entanglement between different single-particle modes.

    “The condition also disallows entanglement between different single-particle modes, as would be expected for a condition of classicality.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning

    Preparing the ground state of a classical Ising model by quantum annealing, adiabatically quenching a transverse field, is expected to be quantum.

    “However, preparing that same state by quantum annealing, adiabatically quenching a transverse field, is expected to be quantum.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning

    Lloyd's digital quantum simulator is effectively a universal quantum computer.

    “Whilst going by the name simulator, it is effectively a universal quantum computer.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning

    The D-wave device's primary use seems to be solving optimisation problems embedded in the Ising ground state, rather than comparing this to a real physical system.

    “We would agree, since its primary use seems to be in solving optimisation problems embedded in the Ising ground state, rather than comparing this to a real physical system.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 20
  • May combine two claims. 13

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

    Interpretationreasoning

    A Bose-Einstein condensate, or a Poissonian mixture of different occupation numbers, or a coherent number superposition of unknown phase, is labelled classical by the paper's definition.

    “In these cases, the single occupied modefunction evolves according to the Gross-Pitaevskii equation and we would label the system as classical.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    Guaranteed accuracy allows assured interpretation of the results of the operation without reference to some real system.

    “A consequence of this guaranteed accuracy is that it allows assured interpretation of the results of the operation, the information obtained about a mathematical function, without reference to some real system.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    If the accuracy with which a device simulates a model can be arbitrarily controlled and guaranteed, it is often elevated to the status of a computer.

    “If the accuracy with which a device simulates a model can be arbitrarily controlled and guaranteed then it is often elevated to the status of a computer, a name that reflects our trust in the device.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisenone given

    Analogue simulators are devices whose Hamiltonians can be engineered to approximate those of a subset of models put forward to describe a real system.

    “They are devices whose Hamiltonians can be engineered to approximate those of a subset of models put forward to describe a real system.”
    Quote in the paperSubstantial claim

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

    Interpretationnone given

    The operation of room-temperature semiconductor devices used to perform every-day computing are classical according to the paper's definition.

    “Reassuringly, the operation of the room-temperature semiconductor devices used to perform every-day computing are classical according to the definition.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    Analogue quantum simulators are the most easily scaled quantum simulators and so are likely to be used in the near future to simulate large systems.

    “For this discussion we focus on analogue quantum simulators, because they are the most easily scaled quantum simulators and so are likely to be used in the near future to simulate large systems.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The other crucial purpose of a simulator is to reveal information about a model and compare this to the behaviour of the real system of interest.

    “This other crucial purpose of a simulator is to reveal information about a model and compare this to the behaviour of the real system of interest.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    If the capability of performing tests of simulators lags behind the development of the simulator, then our confidence must naturally lag.

    “If the capability of performing such tests lags behind the development of the simulator, then so naturally must our confidence.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation

    It would be incorrect to say that such tests verify the accuracy of a simulator; a simulator could have significant errors yet pass these tests.

    “It would be incorrect, however, to say that such tests verify the accuracy of a simulator.A simulator could have significant errors yet pass these tests.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationcitation

    A simulator might be accurate in regimes where accurate analytical or classical numerical results exist, but more sensitive to errors in regimes difficult to treat with other methods, e.g. near phase transitions.

    “It might be that the simulator is accurate in the regimes in which we have accurate analytical or classical numerical results, but is more sensitive to errors in regimes that are difficult to treat with other methods, e.g.near phase transitions, perhaps for the same reason.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    Confidence depends on the eventual goal of our use of the simulator.

    “Further, confidence depends on the eventual goal of our use of the simulator.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Secondly, experimentalists demonstrate a high level of control and flexibility with a simulator, performing some of the simple fail-able tests mentioned above.

    “Secondly, experimentalists demonstrate a high level of control and flexibility with a simulator, performing some of the simple fail-able tests mentioned above [, , ].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [, , ]

      Not checked in the free run.

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

    Interpretationcitation

    Quantum simulation is transitioning from a theoretical dream into a credible possibility.

    “At the time of writing, astonishing levels of control in proof-of-principle experiments (cf. the above references and citations within) suggest that quantum simulation is transitioning from a theoretical dream into a credible possibility.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    Trustworthiness is not a clear-cut topic established upon the initial development of a simulator; instead it is the result of a complex, time-consuming process in the period that follows.

    “In this sense trustworthiness is not a clear-cut topic that is established upon the initial development of a simulator.Instead, it is the result of a complex, time-consuming process in the period that follows.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    Since for simulation we do not always have verifiability, we are not discussing objective properties of devices, but our understanding of them.

    “They indicate that, since for simulation we do not always have verifiability, we are not discussing objective properties of devices, but our understanding of them.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    The purpose of the device is crucial to how it is assessed.

    “It becomes clear that the purpose of the device is crucial to how it is assessed, explaining our highlighting the purpose of a simulator alongside its definition.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    It is difficult for experiments to verify a particular use of a model; rather successful experiments merely declare the model 'not yet false'.

    “It is difficult for experiments to verify a particular use of the model, rather successful experiments merely declare the model 'not yet false' .”
    Quote in the paperNot a substantial claim

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

    Premisenone given

    Calculating the quantity of interest within either system (displacement or time) reduces within the model to calculating a square root.

    “Calculating the quantity of interest within either system, displacement or time, respectively, reduces within the model to calculating a square root.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    There is no guarantee that a classical device or algorithm will not sometime in the future be devised to efficiently study some subset of the above quantum models.

    “It must be stated, however, that there is no guarantee that a classical device or algorithm will not sometime in the future be devised to efficiently study some subset of the above quantum models.”
    Quote in the paperNot a substantial claim

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

    Interpretationreasoning

    Quantum simulators cannot truly be useful until some level of trust is established.

    “since quantum simulators cannot truly be useful until some level of trust is established.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    For the above reasons, quantum devices are expected to be crucial for large network models featuring Fermions or frustration and strong entanglement, or nonnetwork based many-body models featuring states with strong correlations that are difficult to describe with DFT.

    “For the above reasons, quantum devices are expected to be crucial for large network (e.g.lattice) models, featuring Fermions or frustration and strong entanglement, or nonnetwork based many-body models featuring states with strong correlations that are difficult to describe with DFT.”
    Quote in the paperNot a substantial claim

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

    Interpretationnone given

    The simulation of many quantum models can be easy using classical devices and thus not in need of a quantum simulator.

    “This does not of course prohibit the simulation of many quantum models from being easy using classical devices and thus not in need of a quantum simulator.”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    Hauke et al. proposed a set of requirements for a quantum simulator, an alternative to Cirac and Zoller's, that focuses on establishing the reliability and efficiency of a simulator, and the connection between these two properties.

    “Hauke et al. proposed a set of requirements for a quantum simulator, an alternative to Cirac and Zoller's, that focuses on establishing the reliability and efficiency of a simulator, and the connection between these two properties [].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites []

      Not checked in the free run.

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

    Premisecitation

    In 2014 the USA bobsleigh team won Olympic bronze with a machine designed almost entirely virtually, using simulation to optimise aerodynamic performance without a wind tunnel.

    “Simulation was used to optimise the aerodynamic performance without the need for a wind tunnel.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [ ]

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Comparing a model's simulation to the real system allows inference of whether the model provides a good description of the system and whether the results bear relevance to the real world.

    “This then allows us to infer whether or not the model provides a 'good' description of the system in the first place and whether or not the results bear any relevance to the real world.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    If any of the above tests fail beyond an acceptable accuracy, then we do not trust the simulation results; if a simulator passes all tests, then we may take this as support for the accuracy of that simulator.

    “If any of the above tests fail beyond an acceptable accuracy, then we do not trust the simulation results.If a simulator passes all tests, then we may take this as support for the accuracy of that simulator.”
    Quote in the paperSubstantial claim

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

    Interpretationreasoning

    It is possible that the experimental difficulty of scaling up quantum simulation hardware might cause an overhead such that a quantum device does not surpass the accuracy obtained by a classical algorithm that in principle does not scale as well but runs on ever-improving hardware obeying Moore's law.

    “It is possible that the experimental difficulty of scaling up quantum simulation hardware might cause an overhead such that a quantum device does not surpass the accuracy obtained by a classical algorithm that in principle does not scale as well but runs on ever-improving hardware obeying Moore's law.”
    Quote in the paperNot a substantial claim
27 of 27

  • The paper relies on this without support.

    Confidence in each simulator is a matter of perspective and is not objective.

    “However, the confidence in each simulator is a matter of perspective.It is not objective.”

  • The paper relies on this without support.

    Many centuries ago, we would only have trusted the abacus to perform such a calculation, since its principles were well understood and square-root algorithms with assured convergence were known even to the Babylonians.

    “Many centuries ago, we would only have trusted the abacus to perform such a calculation, since its principles were well understood and square-root algorithms with assured convergence were known even to the Babylonians.”

  • The paper relies on this without support.

    Nowadays, we would all choose the calculator or a solid-state equivalent.

    “Nowadays, we would all choose the calculator or a solid-state equivalent.”

  • The paper relies on this without support.

    Confidence in the simulation could have been established by testing the analogue simulator against the abacus.

    “Confidence in the simulation could have been established by testing the analogue simulator against the abacus.”
4 of 4

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 quantum simulator's primary role is to divulge details of a conceptual mathematical function associated with a physical model.

    “The quantum simulator's primary role is to divulge details of a conceptual mathematical function associated with a physical model [51].”

    From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [51]

  • Grover's algorithm can act as a subroutine of many complex algorithms used in computational biology for data processing, including protein sequence comparison, neuronal modeling of intracellular Ca2+ dynamics, and quantum machine learning algorithms.

    “It can act as a subroutine of many complex algorithms used in computational biology for data processing, such as advanced proposition in protein sequence comparison [49], the neuronal version to understand the intracellular Ca 2 + dynamics [50], and leading algorithms in the quantum domain of machine learning [51].”

    From Quantum Computing in the Next-Generation Computational Biology Landscape: From Protein Folding to Molecular Dynamics (2024) · cites this paper as [51]

    The passages from “What are quantum simulators?” and the References (page numbers unavailable) discuss quantum simulation and related work, but do not address the attributed applications. Searches for Grover, protein sequence comparison, intracellular calcium dynamics, and quantum machine learning found no passage supporting the claim. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

Cites

Flagged first, then by citations

Research works printed but not linked: 9

  1. Brewster D: Planetary machines. In The Edinburgh Encyclopedia Vol 16. William Blackwood and Proprietors, Edinburgh; 1830:624.
  2. Cairns WJ, Crank J, Lloyd EC: Some improvements in the construction of a small scale differential analyser and a review of recent applications. Technical report 27/44, Armament Research Department Theoretical Research; 1944. UK National Archives reference DEFE 15/751 C20779.
  3. Angelakis DG, Santos MF, Bose S: Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays. Phys. Rev. A 2007., 76: Article ID 031805 Article ID 031805
  4. Ashcroft NW, Mermin D: Solid State Physics. Holt, Rinehardt and Winston, New York; 1976.
  5. Barceló C, Liberati S, Visser M: Analogue gravity. Living Rev. Relativ. 2005., 8: Article ID 12 Article ID 12
  6. Anderson PW, Lee PA, Randeria M, Rice TM, Trivedi N, Zhang FC: The physics behind high-temperature superconducting cuprates: the ‘plain vanilla’ version of RVB. J. Phys. Condens. Matter 2004., 16: Article ID R755 Article ID R755
  7. Biamonte JD, Clark SR, Jaksch D: Categorical tensor network states. AIP Adv. 2011., 1: Article ID 042172 Article ID 042172
  8. Orús R: A practical introduction to tensor networks: matrix product states and projected entangled pair states. arXiv:1306.2164. · arXiv
  9. Pollet L: Recent developments in quantum Monte Carlo simulations with applications for cold gases. Rep. Prog. Phys. 2012., 75: Article ID 094501 Article ID 094501

Cited by

Sorted by citations

Related

Authors
Johnson, T. H., Clark, S. R., & Jaksch, D.
Affiliations
Centre for Quantum Technologies (SG)
Corresponding author
Johnson, Tomi H
ORCID
Venue
EPJ Quantum Technology
Publisher
Springer Science and Business Media LLC
Published
2014-07-23
Volume
1
Issue
1
ISSN
2196-0763 (ISSN-L)
DOI
10.1140/epjqt10
OpenAlex
W1965107402
Cited by
127
References
129
Citations by year
2026: 5 · 2025: 8 · 2024: 12 · 2023: 9 · 2022: 7 · 2021: 16 · 2020: 9 · 2019: 16 · 2018: 16 · 2017: 10 · 2016: 10 · 2015: 8 · 2014: 1
FWCI
9.64
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • EPJ Quantum Technology (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • National University of Singapore (submittedVersion)
  • Explore Bristol Research (submittedVersion)
  • arXiv (Cornell University)
Funders
National Research Foundation
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum simulators, quantum simulation, quantum computing, simulation accuracy, model systems

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