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arxiv: 2606.02721 · v2 · pith:NDOS6PXRnew · submitted 2026-06-01 · ❄️ cond-mat.str-el · cond-mat.mes-hall· cond-mat.quant-gas· hep-lat· quant-ph

Simulating Condensed Matter Physics on Quantum Hardware

Ruizhe Shen , Tianqi Chen , Tommy Tai , Jin Ming Koh , Pouyan Ghaemi , Ching Hua Lee This is my paper

Pith reviewed 2026-06-28 12:34 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mes-hallcond-mat.quant-gashep-latquant-ph
keywords quantum simulationcondensed matter physicsnoisy quantum devicesfault-tolerant quantum computingstrongly correlated systemstopological phasesnon-equilibrium dynamicsdigital quantum simulation
0
0 comments X

The pith

Noisy quantum simulations of condensed matter already serve as prototypes for the encodings and error controls required in future fault-tolerant machines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review surveys recent progress using quantum hardware to simulate condensed matter phenomena including strongly correlated systems, topological phases, and non-equilibrium dynamics. It covers major platforms such as superconducting qubits, trapped ions, ultracold atoms, Rydberg arrays, photonic systems, and moiré materials, then presents the basic ingredients of digital quantum simulation before examining representative applications and key methodological tools. The central claim is that these current noisy experiments function as testbeds whose encodings, diagnostic protocols, and error-control strategies will directly transfer to fault-tolerant quantum simulation. A reader would care because successful scaling of these methods could enable reliable modeling of complex materials that classical computers struggle with. The review positions analog experiments as useful benchmarks alongside the primary focus on gate-based digital approaches.

Core claim

The paper establishes that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation of condensed matter phenomena.

What carries the argument

The review's organized survey of hardware platforms, basic digital quantum simulation ingredients, applications spanning ground-state problems through open-system physics, and methodological tools used in current workflows.

If this is right

  • Diagnostic protocols validated on noisy devices will scale directly to larger error-corrected systems for ground-state and dynamics problems.
  • Encodings developed for topological phases and strongly correlated matter will form the basis of fault-tolerant implementations.
  • Methodological tools summarized will become standard components in future quantum-simulation workflows.
  • Analog experiments on ultracold atoms and Rydberg arrays will continue to provide independent benchmarks for digital approaches.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Investment in current noisy hardware therefore carries long-term value for building fault-tolerant simulators rather than serving only short-term publicity.
  • The inclusion of high-energy-physics-inspired simulations suggests potential for cross-field transfer of simulation techniques between condensed matter and particle physics.
  • A natural extension would be quantitative mapping of current error rates in these prototypes onto the thresholds required for fault-tolerant operation on specific condensed-matter Hamiltonians.

Load-bearing premise

The review assumes its selection of representative hardware platforms and condensed-matter applications captures the current state and trajectory of the field without major omissions.

What would settle it

A major condensed-matter simulation result achieved on an unmentioned hardware platform whose encodings and error strategies do not align with those highlighted in the review would undermine the prototype claim.

Figures

Figures reproduced from arXiv: 2606.02721 by Ching Hua Lee, Jin Ming Koh, Pouyan Ghaemi, Ruizhe Shen, Tianqi Chen, Tommy Tai.

Figure 1
Figure 1. Figure 1: FIG. 1. Representative platforms for quantum simulation. (a) Superconducting qubits arranged in a two-dimensional lattice [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Experimental demonstrations of exactly solved SPT and AKLT-type quantum states on noisy quantum hardware. (a) [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Quantum imaginary-time evolution and error-mitigated simulation of quantum phases. (a) Schematic illustration [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Representative quantum hardware demonstrations of variational quantum solvers. (a) First proof-of-principle hard [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Circuit implementation of the trotterized unitary [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Strongly-correlated phases realized in pioneering analog quantum simulators. (a) Strongly correlated electronic phases [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Circuit-native routes to topological phenomena on digital quantum processors. [PITH_FULL_IMAGE:figures/full_fig_p032_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Quantum hardware demonstrations of topological order and anyonic phenomena. (a) Top: Step-by-step preparation [PITH_FULL_IMAGE:figures/full_fig_p038_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Quantum simulations of prethermalization. (a) Trapped-ion long-ranged Ising dynamics exhibiting a memoryful [PITH_FULL_IMAGE:figures/full_fig_p040_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Early experimental realizations of time-crystalline order in driven many-body systems. (a) Disorder-assisted discrete [PITH_FULL_IMAGE:figures/full_fig_p041_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Larger-period temporal order in quantum-simulation platforms. (a) Robust large-period 4 [PITH_FULL_IMAGE:figures/full_fig_p044_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Pioneering experimental probes of many-body localization (MBL) in quantum simulators. (a) Spatio-temporal [PITH_FULL_IMAGE:figures/full_fig_p045_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Further experimental demonstrations of many-body localizations (MBL). (a) Stark (tilt-induced) MBL in a disorder [PITH_FULL_IMAGE:figures/full_fig_p047_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Experimental realizations of quantum many-body scars (QMBS) across different quantum platforms. (a)Rydberg-atom [PITH_FULL_IMAGE:figures/full_fig_p049_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Experimental realizations of non-Hermitian quantum physics on digital and analog quantum platforms. (a) Digital [PITH_FULL_IMAGE:figures/full_fig_p052_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Digital and analog approaches to simulating open quantum systems. (a) Analog realization of engineered dissipation [PITH_FULL_IMAGE:figures/full_fig_p052_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Experimental demonstrations of measurement-induced phase transitions in monitored quantum circuits. (a) Digital [PITH_FULL_IMAGE:figures/full_fig_p054_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Simulations of adaptive quantum circuits on the IBM quantum processor (a) Top: schematic of the adaptive Bernoulli [PITH_FULL_IMAGE:figures/full_fig_p055_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Experimental milestones in digital and analog quantum simulation of lattice gauge theories. (a) Real-time particle [PITH_FULL_IMAGE:figures/full_fig_p061_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Real-time string dynamics in higher-dimensional lattice gauge theories. (a) Digital quantum simulation of real-time [PITH_FULL_IMAGE:figures/full_fig_p062_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21. Large-scale Floquet quantum simulation on a superconducting quantum processor. (a) Schematic of the Floquet [PITH_FULL_IMAGE:figures/full_fig_p064_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Illustration of the quantum circuit recompilation. (i) Classical optimization stage. A target circuit [PITH_FULL_IMAGE:figures/full_fig_p069_22.png] view at source ↗
read the original abstract

Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a review surveying recent progress in quantum-hardware-based simulations of condensed matter physics. It first reviews major hardware platforms (superconducting qubits, trapped ions, ultracold atoms, Rydberg arrays, photonic systems, and moiré quantum materials), then introduces the basic ingredients of digital quantum simulation, discusses representative applications spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations, and finally summarizes key methodological tools. The central perspective is that present noisy quantum simulations serve not only as near-term demonstrations but also as prototypes for the encodings, diagnostic protocols, and error-control strategies required for future fault-tolerant quantum simulation.

Significance. If the survey is accurate and balanced, the review would provide a useful synthesis for the condensed-matter and quantum-information communities by connecting hardware developments with specific physics applications and methodological advances. The forward-looking framing of NISQ-era work as prototyping for fault-tolerant simulation offers helpful context without advancing new technical claims.

minor comments (2)
  1. [Abstract] Abstract: the high-level overview of platforms and applications is clear, but adding a brief statement on the approximate time window or number of works surveyed would help readers gauge the review's currency and scope.
  2. The transition from the hardware-platforms section to the applications section would benefit from an explicit roadmap sentence to improve navigation for readers focused on specific condensed-matter topics.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our manuscript as a useful synthesis for the condensed-matter and quantum-information communities. The recommendation for minor revision is noted. However, the report lists no specific major comments requiring response.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript is a review surveying hardware platforms and applications in quantum simulation of condensed matter. It advances no original derivations, equations, fitted parameters, or quantitative predictions. All content consists of summaries of external literature with forward-looking synthesis; no load-bearing step reduces by construction to the paper's own inputs or self-citations. This is the expected outcome for a non-derivational survey paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper, the work introduces no new free parameters, axioms, or invented entities; it summarizes prior literature on quantum simulation.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    quant-ph 2026-06 unverdicted novelty 6.0

    Derives an analytical mapping from hybrid unitary-projective qutrit evolution to target non-Hermitian two-body interactions for pseudo-spins in a Zeno subspace, validated numerically.

Reference graph

Works this paper leans on

300 extracted references · 12 canonical work pages · cited by 1 Pith paper · 5 internal anchors

  1. [1]

    Yang, Z.-X

    B. Yang, Z.-X. Hu, C. H. Lee, and Z. Papi´ c, Generalized pseudopotentials for the anisotropic fractional quantum hall effect, Phys. Rev. Lett.118, 146403 (2017)

    2017

  2. [2]

    Z. Liu, A. Gromov, and Z. Papi´ c, Geometric quench and nonequilibrium dynamics of fractional quantum hall states, Phys. Rev. B98, 155140 (2018)

    2018

  3. [3]

    M. F. Lapa, A. Gromov, and T. L. Hughes, Geometric quench in the fractional quantum hall effect: Exact so- lution in quantum hall matrix models and comparison with bimetric theory, Phys. Rev. B99, 075115 (2019)

    2019

  4. [4]

    Liang, Z

    J. Liang, Z. Liu, Z. Yang, Y. Huang, U. Wurstbauer, C. R. Dean, K. W. West, L. N. Pfeiffer, L. Du, and A. Pinczuk, Evidence for chiral graviton modes in frac- tional quantum Hall liquids, Nature628, 78 (2024)

    2024

  5. [5]

    Pinczuk, B

    A. Pinczuk, B. S. Dennis, L. N. Pfeiffer, and K. W. West, Observation of collective excitations in the frac- tional quantum Hall effect, Phys. Rev. Lett.70, 3983 (1993)

    1993

  6. [6]

    P. M. Platzman and S. He, Resonant raman scattering from magneto rotons in the fractional quantum Hall liq- uid, Phys. Scr.T66, 167 (1996)

    1996

  7. [7]

    M. Kang, A. Pinczuk, B. S. Dennis, L. N. Pfeiffer, and K. W. West, Observation of multiple magnetorotons in the fractional quantum Hall effect, Phys. Rev. Lett.86, 2637 (2001)

    2001

  8. [8]

    I. V. Kukushkin, J. H. Smet, V. W. Scarola, V. Uman- sky, and K. von Klitzing, Dispersion of the excitations of fractional quantum Hall states, Science324, 1044 (2009)

    2009

  9. [9]

    Maciejko, B

    J. Maciejko, B. Hsu, S. A. Kivelson, Y. Park, and S. L. Sondhi, Field theory of the quantum hall nematic tran- sition, Phys. Rev. B88, 125137 (2013)

    2013

  10. [10]

    Werschnik and E

    J. Werschnik and E. K. U. Gross, Quantum optimal control theory, J. Phys. B: At. Mol. Opt. Phys.40, R175 (2007), arXiv:0707.1883 [quant-ph]

    Pith/arXiv arXiv 2007

  11. [11]

    Petersen and D

    I. Petersen and D. Dong, Quantum control theory and applications: a survey, IET Control Theory Appl.4, 2651 (2010)

    2010

  12. [12]

    Rahmani, Quantum dynamics with an ensemble of hamiltonians, Mod

    A. Rahmani, Quantum dynamics with an ensemble of hamiltonians, Mod. Phys. Lett. B27, 1330019 (2013)

    2013

  13. [13]

    Wecker, M

    D. Wecker, M. B. Hastings, and M. Troyer, Training a quantum optimizer, Phys. Rev. A94, 022309 (2016)

    2016

  14. [14]

    A Quantum Approximate Optimization Algorithm

    E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv preprint arXiv:1411.4028 10.48550/arXiv.1411.4028 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1411.4028 2014

  15. [15]

    Farhi and A

    E. Farhi and A. W. Harrow, Quantum supremacy through the quantum approximate optimiza- tion algorithm, arXiv preprint arXiv:1602.07674 10.48550/arXiv.1602.07674 (2016)

    work page doi:10.48550/arxiv.1602.07674 2016

  16. [16]

    Z.-C. Yang, A. Rahmani, A. Shabani, H. Neven, and C. Chamon, Optimizing variational quantum algorithms using pontryagin’s minimum principle, Phys. Rev. X7, 021027 (2017)

    2017

  17. [17]

    Z. Wang, S. Hadfield, Z. Jiang, and E. G. Rieffel, Quan- tum approximate optimization algorithm for maxcut: A fermionic view, Phys. Rev. A97, 022304 (2018)

    2018

  18. [18]

    Zhou, S.-T

    L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near- term devices, Phys. Rev. X10, 021067 (2020)

    2020

  19. [19]

    S.-H. Lin, R. Dilip, A. G. Green, A. Smith, and F. Poll- mann, Real- and imaginary-time evolution with com- pressed quantum circuits, PRX Quantum2, 010342 (2021)

    2021

  20. [20]

    T. Y. Ng, J. M. Koh, and D. E. Koh, Analytical expres- sions for the quantum approximate optimization algo- rithm and its variants (2024), arXiv:2411.09745 [quant- ph]

    arXiv 2024

  21. [21]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars in a landau level on a thin torus, Phys. Rev. B102, 195150 (2020)

    2020

  22. [22]

    Moudgalya, A

    S. Moudgalya, A. Prem, R. Nandkishore, N. Regnault, and B. A. Bernevig, Thermalization and its absence within krylov subspaces of a constrained hamiltonian (2019), arXiv:1910.14048 [cond-mat.str-el]

    arXiv 2019

  23. [23]

    Feiguin, S

    A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, Interact- ing anyons in topological quantum liquids: The golden chain, Phys. Rev. Lett.98, 160409 (2007)

    2007

  24. [24]

    Saravanan and S

    V. Saravanan and S. M. Saeed, Pauli error propagation- based gate rescheduling for quantum circuit error miti- gation, IEEE Trans. Quantum Eng.3, 1 (2022)

    2022

  25. [25]

    Javadi-Abhari, M

    A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, and J. M. Gambetta, Quantum computing with Qiskit (2024), arXiv:2405.08810 [quant-ph]

    Pith/arXiv arXiv 2024

  26. [26]

    M. G. Davis, E. Smith, A. Tudor, K. Sen, I. Siddiqi, and C. Iancu, Towards optimal topology aware quantum cir- 92 cuit synthesis, inProc. 2020 IEEE Int. Conf. Quantum Comput. Eng. (QCE)(2020) pp. 223–234

    2020

  27. [27]

    J. Haah, M. B. Hastings, R. Kothari, and G. H. Low, Quantum algorithm for simulating real time evolution of lattice hamiltonians, SIAM J. Comput.52, FOCS18 (2023)

    2023

  28. [28]

    A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of trotter error with commutator scaling, Phys. Rev. X11, 011020 (2021)

    2021

  29. [29]

    Kirmani, A

    A. Kirmani, A. A. Allocca, J.-X. Zhu, A. Rahmani, S. Ganeshan, and P. Ghaemi, Measuring the hall vis- cosity of the laughlin state on noisy quantum computers (2025), arXiv:2512.09982 [cond-mat.str-el]

    arXiv 2025

  30. [30]

    Harley, I

    D. Harley, I. Datta, F. R. Klausen, A. Bluhm, D. S. Fran¸ ca, A. H. Werner, and M. Christandl, Going be- yond gadgets: the importance of scalability for analogue quantum simulators, Nat. Commun.15, 6527 (2024)

    2024

  31. [31]

    Trivedi, A

    R. Trivedi, A. F. Rubio, and J. I. Cirac, Quantum ad- vantage and stability to errors in analogue quantum sim- ulators, Nat. Commun.15, 6507 (2024)

    2024

  32. [32]

    Morgado and S

    M. Morgado and S. Whitlock, Quantum simulation and computing with rydberg-interacting qubits, AVS Quan- tum Sci.3, 023501 (2021), arXiv:2011.03031 [quant-ph]

    arXiv 2021

  33. [33]

    Defenu, T

    N. Defenu, T. Donner, T. Macr` ı, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys.95, 035002 (2023)

    2023

  34. [34]

    Aidelsburger, S

    M. Aidelsburger, S. Nascimbene, and N. Goldman, Ar- tificial gauge fields in materials and engineered systems, C. R. Phys.19, 394 (2018)

    2018

  35. [35]

    Wiese, Ultracold quantum gases and lattice sys- tems: quantum simulation of lattice gauge theories, Ann

    U.-J. Wiese, Ultracold quantum gases and lattice sys- tems: quantum simulation of lattice gauge theories, Ann. Phys. (Berl.)525, 777 (2013), arXiv:1305.1602 [cond-mat.quant-gas]

    Pith/arXiv arXiv 2013

  36. [36]

    Dalmonte and S

    M. Dalmonte and S. Montangero, Lattice gauge the- ory simulations in the quantum information era, Con- temp. Phys.57, 388 (2016), arXiv:1602.03776 [cond- mat.quant-gas]

    Pith/arXiv arXiv 2016

  37. [37]

    Kato, On the adiabatic theorem of quantum mechan- ics, J

    T. Kato, On the adiabatic theorem of quantum mechan- ics, J. Phys. Soc. Jpn.5, 435 (1950)

    1950

  38. [38]

    Quantum Computation by Adiabatic Evolution

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, Quantum computation by adiabatic evolution, arXiv preprint quant-ph/0001106 10.48550/arXiv.quant- ph/0001106 (2000)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.quant- 2000

  39. [39]

    A. J. Leggett, Bose-einstein condensation in the alkali gases: Some fundamental concepts, Rev. Mod. Phys. 73, 307 (2001)

    2001

  40. [40]

    M. C. Gutzwiller, Effect of correlation on the ferromag- netism of transition metals, Phys. Rev. Lett.10, 159 (1963)

    1963

  41. [41]

    M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B40, 546 (1989)

    1989

  42. [42]

    Capogrosso-Sansone, S ¸

    B. Capogrosso-Sansone, S ¸. G. S¨ oyler, N. Prokof’ev, and B. Svistunov, Monte carlo study of the two-dimensional Bose-Hubbard model, Phys. Rev. A77, 015602 (2008)

    2008

  43. [43]

    Endres, M

    M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M. C. Ba˜ nuls, L. Pol- let, and I. Bloch, Observation of correlated particle-hole pairs and string order in low-dimensional Mott insula- tors, Science334, 200 (2011)

    2011

  44. [44]

    F. C. Zhang and T. M. Rice, Effective hamiltonian for the superconducting Cu oxides, Phys. Rev. B37, 3759 (1988)

    1988

  45. [45]

    T. A. Hilker, G. Salomon, F. Grusdt, A. Omran, M. Boll, E. Demler, I. Bloch, and C. Gross, Revealing hidden antiferromagnetic correlations in doped hubbard chains via string correlators, Science357, 484 (2017)

    2017

  46. [46]

    C. S. Chiu, G. Ji, A. Bohrdt, M. Xu, M. Knap, E. Dem- ler, F. Grusdt, M. Greiner, and D. Greif, String patterns in the doped hubbard model, Science365, 251 (2019)

    2019

  47. [47]

    Wecker, M

    D. Wecker, M. B. Hastings, N. Wiebe, B. K. Clark, C. Nayak, and M. Troyer, Solving strongly correlated electron models on a quantum computer, Phys. Rev. A 92, 062318 (2015)

    2015

  48. [48]

    Xiang, K

    Z.-C. Xiang, K. Huang, Y.-R. Zhang, T. Liu, Y.-H. Shi, C.-L. Deng, T. Liu, H. Li, G.-H. Liang, Z.-Y. Mei, H. Yu, G. Xue, Y. Tian, X. Song, Z.-B. Liu, K. Xu, D. Zheng, F. Nori, and H. Fan, Simulating chern in- sulators on a superconducting quantum processor, Nat. Commun.14, 5433 (2023)

    2023

  49. [49]

    X. Xiao, J. K. Freericks, and A. F. Kemper, Robust measurement of wave function topology on nisq quan- tum computers, Quantum7, 987 (2023)

    2023

  50. [50]

    Viyuela, A

    O. Viyuela, A. Rivas, S. Gasparinetti, A. Wallraff, S. Filipp, and M. A. Mart´ ın-Delgado, Observation of topological uhlmann phases with superconducting qubits, npj Quantum Inf.4, 10 (2018)

    2018

  51. [51]

    J. M. Koh, T. Tai, and C. H. Lee, Simulation of interaction-induced chiral topological dynamics on a digital quantum computer, Phys. Rev. Lett.129, 140502 (2022)

    2022

  52. [52]

    J. M. Koh, T. Tai, and C. H. Lee, Realization of higher- order topological lattices on a quantum computer, Nat. Commun.15, 5807 (2024)

    2024

  53. [53]

    M. D. Schroer, M. H. Kolodrubetz, W. F. Kindel, M. Sandberg, J. Gao, M. R. Vissers, D. P. Pappas, A. Polkovnikov, and K. W. Lehnert, Measuring a topo- logical transition in an artificial spin-1/2 system, Phys. Rev. Lett.113, 050402 (2014)

    2014

  54. [54]

    F. Mei, Q. Guo, Y.-F. Yu, L. Xiao, S.-L. Zhu, and S. Jia, Digital simulation of topological matter on pro- grammable quantum processors, Phys. Rev. Lett.125, 160503 (2020)

    2020

  55. [55]

    T. Y. Ng, Y. Wang, W. J. Chan, R. Shen, T. Chen, and C. H. Lee, Digital simulation of non-hermitian knotted bands on quantum hardware, arXiv preprint arXiv:2604.26914 10.48550/arXiv.2604.26914 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.26914 2026

  56. [56]

    X. Xiao, J. K. Freericks, and A. F. Kemper, Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware, Quantum5, 553 (2021)

    2021

  57. [57]

    M. J. Ranˇ ci´ c, Exactly solving the kitaev chain and gen- erating majorana-zero-modes out of noisy qubits, Sci. Rep.12, 19882 (2022)

    2022

  58. [58]

    J. P. T. Stenger, G. Ben-Shach, D. Pekker, and N. T. Bronn, Simulating spectroscopy experiments with a su- perconducting quantum computer, Phys. Rev. Res.4, 043106 (2022)

    2022

  59. [59]

    K. J. Sung, M. J. Ranˇ ci´ c, O. T. Lanes, and N. T. Bronn, Simulating majorana zero modes on a noisy quantum processor, Quantum Sci. Technol.8, 025010 (2023)

    2023

  60. [60]

    Google Quantum AI and Collaborators, Non-abelian braiding of graph vertices in a superconducting proces- sor, Nature618, 264 (2023)

    2023

  61. [61]

    J. M. Koh, W.-T. Xue, T. Tai, D. E. Koh, and C. H. Lee, Interacting non-hermitian edge and cluster bursts on a digital quantum processor, arXiv preprint 93 arXiv:2503.14595 10.48550/arXiv.2503.14595 (2025)

    work page doi:10.48550/arxiv.2503.14595 2025

  62. [62]

    Qi, Generic wave-function description of fractional quantum anomalous hall states and fractional topolog- ical insulators, Phys

    X.-L. Qi, Generic wave-function description of fractional quantum anomalous hall states and fractional topolog- ical insulators, Phys. Rev. Lett.107, 126803 (2011)

    2011

  63. [63]

    Huang and D

    Z. Huang and D. P. Arovas, Entanglement spectrum and wannier center flow of the hofstadter problem, Phys. Rev. B86, 245109 (2012)

    2012

  64. [64]

    C. H. Lee and P. Ye, Free-fermion entanglement spec- trum through wannier interpolation, Phys. Rev. B91, 085119 (2015)

    2015

  65. [65]

    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized hall conductance in a two- dimensional periodic potential, Phys. Rev. Lett.49, 405 (1982)

    1982

  66. [66]

    parity anomaly

    F. D. M. Haldane, Model for a quantum hall effect with- out landau levels: Condensed-matter realization of the “parity anomaly”, Phys. Rev. Lett.61, 2015 (1988)

    2015

  67. [67]

    Y. Gu, C. H. Lee, X. Wen, G. Y. Cho, S. Ryu, and X.- L. Qi, Holographic duality between (2+ 1)-dimensional quantum anomalous hall state and (3+ 1)-dimensional topological insulators, Phys. Rev. B94, 125107 (2016)

    2016

  68. [68]

    K. Sun, Z. Gu, H. Katsura, and S. Das Sarma, Nearly flatbands with nontrivial topology, Phys. Rev. Lett. 106, 236803 (2011)

    2011

  69. [69]

    Regnault and B

    N. Regnault and B. A. Bernevig, Fractional chern insu- lator, Phys. Rev. X1, 021014 (2011)

    2011

  70. [70]

    C. H. Lee and X.-L. Qi, Lattice construction of pseudopotential hamiltonians for fractional chern insulators, arXiv preprint arXiv:1308.6831 10.48550/arXiv.1308.6831 (2013)

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1308.6831 2013

  71. [71]

    C. H. Lee, Many-body topological and skin states with- out open boundaries, Phys. Rev. B104, 195102 (2021)

    2021

  72. [72]

    J. Niu, T. Yan, Y. Zhou, Z. Tao, X. Li, W. Liu, L. Zhang, H. Jia, S. Liu, Z. Yan, Y. Chen, and D. Yu, Simulation of higher-order topological phases and re- lated topological phase transitions in a superconducting qubit, Sci. Bull.66, 1168 (2021)

    2021

  73. [73]

    Bianco and R

    R. Bianco and R. Resta, Mapping topological order in coordinate space, Phys. Rev. B84, 241106 (2011)

    2011

  74. [74]

    M. B. Hastings and T. A. Loring, Almost commuting matrices, localized Wannier functions, and the quantum Hall effect, J. Math. Phys.51, 015214 (2010)

    2010

  75. [75]

    Prodan, B

    E. Prodan, B. Leung, and J. Bellissard, The non- commutativenth-chern number (n⩾1), J. Phys. A Math. Theor.46, 485202 (2013)

    2013

  76. [76]

    Xu, Q.-Q

    X.-Y. Xu, Q.-Q. Wang, M. Heyl, J. C. Budich, W.-W. Pan, Z. Chen, M. Jan, K. Sun, J.-S. Xu, Y.-J. Han, C.-F. Li, and G.-C. Guo, Measuring a dynamical topological order parameter in quantum walks, Light Sci. Appl.9, 7 (2020)

    2020

  77. [77]

    Chen, C.-Z

    R. Chen, C.-Z. Chen, B. Zhou, and D.-H. Xu, Finite- size effects in non-hermitian topological systems, Phys. Rev. B99, 155431 (2019)

    2019

  78. [78]

    Yao and Z

    S. Yao and Z. Wang, Edge states and topological invari- ants of non-hermitian systems, Phys. Rev. Lett.121, 086803 (2018)

    2018

  79. [79]

    F. K. Kunst, E. Edvardsson, J. C. Budich, and E. J. Bergholtz, Biorthogonal bulk-boundary correspondence in non-hermitian systems, Phys. Rev. Lett.121, 026808 (2018)

    2018

  80. [80]

    Yokomizo and S

    K. Yokomizo and S. Murakami, Non-bloch band theory of non-hermitian systems, Phys. Rev. Lett.123, 066404 (2019)

    2019

Showing first 80 references.