Pith. sign in

REVIEW 1 major objections 2 minor 74 references

A quantum framework simulates semiconductor optical spectra by discretizing the Brillouin zone and encoding light-matter interactions in second quantization.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-28 09:20 UTC pith:H2KTHZGW

load-bearing objection The paper gives a working quantum-circuit implementation for single-particle semiconductor spectra that matches classical GaAs benchmarks in the noiseless case, with the many-body extension left as a stated future direction. the 1 major comments →

arxiv 2606.04295 v1 pith:H2KTHZGW submitted 2026-06-02 quant-ph

Quantum simulations of ultrafast optical spectroscopy of semiconductors on digital quantum computers in the semi-classical approximation

Mykhailo Klymenko , Bahar Goldozian , Thong Hoang , Jared H. Cole , Muhammad Usman This is my paper
classification quant-ph
keywords quantum simulationsemiconductor spectroscopyoptical absorptionBrillouin zonesecond quantizationNISQ noisemany-body physicslight-matter interaction
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a digital quantum simulation method for ultrafast optical spectroscopy in semiconductors as an alternative to classical semiconductor Bloch equations. It uses Brillouin-zone discretization to model linear absorption, optical gain, temperature effects, and reduced dimensionality, showing quantitative match to classical results for GaAs when noise is absent. Noise from current quantum hardware appears as extra spectral broadening. The approach is built to scale into many-body regimes where classical methods encounter exponential costs.

Core claim

The paper establishes a digital quantum simulation framework for ultrafast optical spectroscopy of semiconductors based on Brillouin-zone discretization and the second-quantization formalism. This framework reproduces linear absorption and optical gain spectra while incorporating Lorentzian broadening, finite-temperature band filling, and reduced-dimensionality effects. Benchmark comparisons with classical simulations for GaAs demonstrate quantitative agreement in the noiseless limit, and realistic NISQ noise manifests as additional scattering that increases spectral broadening.

What carries the argument

Brillouin-zone discretization combined with second-quantization formalism implemented on a digital quantum computer, which encodes the semiconductor band structure, light-matter coupling, and statistical occupation into quantum circuits for spectrum calculation.

Load-bearing premise

The semi-classical approximation together with Brillouin-zone discretization remains sufficient to capture the central elements of semiconductor spectroscopy even when the method is extended beyond the single-particle regime.

What would settle it

Running the quantum circuit for a GaAs absorption spectrum on actual NISQ hardware and comparing the result directly to both the classical semiconductor Bloch equation prediction and experimental data under identical temperature and broadening conditions.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Quantitative agreement with classical methods in the noiseless limit validates the single-particle implementation.
  • Inclusion of NISQ noise produces increased spectral broadening equivalent to additional scattering processes.
  • The same discretization and encoding approach extends directly to many-body regimes.
  • The framework supplies a physically motivated benchmark for quantum computers on problems involving open quantum systems and non-equilibrium dynamics.

Where Pith is reading between the lines

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

  • Extending the method to interacting many-body states could bypass the classical hierarchy problem in semiconductor many-body calculations.
  • The noise-as-scattering mapping suggests that error mitigation techniques developed for this spectroscopy task may transfer to other open-system simulations.
  • Testing the framework on materials with stronger electron-phonon coupling would reveal whether the semi-classical limit breaks before many-body effects dominate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a digital quantum simulation framework for ultrafast optical spectroscopy of semiconductors in the semi-classical approximation. Based on Brillouin-zone discretization and second quantization, the approach serves as a quantum alternative to classical semiconductor Bloch equations. It enables simulations of linear absorption and optical gain spectra that incorporate Lorentzian broadening, finite-temperature band-filling, and reduced-dimensionality effects. Benchmark comparisons for GaAs are reported to show quantitative agreement with classical results in the noiseless limit, while NISQ hardware noise is described as producing additional spectral broadening. The work notes that exponential quantum advantage is not expected in the single-particle regime but positions the framework as naturally extensible to many-body regimes where classical methods encounter hierarchy problems.

Significance. If the reported benchmarks are robust, the manuscript supplies a concrete, physically motivated test case for quantum computers that integrates open quantum systems, light-matter interactions, statistical mechanics, and non-equilibrium dynamics. It offers a scalable model for benchmarking quantum hardware on real-world semiconductor problems even within the current single-particle scope. The forward-looking discussion of many-body extensions addresses a recognized limitation of classical approaches, though this extension remains undemonstrated.

major comments (1)
  1. [Abstract] Abstract: the claim of quantitative agreement between the quantum simulations and classical results for GaAs in the noiseless limit is presented without any supporting equations, error bars, data exclusion rules, or implementation details; this absence is load-bearing for evaluating the central benchmark result.
minor comments (2)
  1. The manuscript would benefit from an explicit statement in the introduction or conclusions clarifying that the many-body extension and associated quantum advantage remain prospective and are not supported by any derivation or test within the present scope.
  2. Notation for the second-quantization operators and the Brillouin-zone discretization grid should be defined consistently in a dedicated methods section to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback. We address the single major comment below and will revise the manuscript to improve clarity and support for the central benchmark claim.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of quantitative agreement between the quantum simulations and classical results for GaAs in the noiseless limit is presented without any supporting equations, error bars, data exclusion rules, or implementation details; this absence is load-bearing for evaluating the central benchmark result.

    Authors: We agree that the abstract, as currently worded, presents the quantitative agreement claim without sufficient qualifiers or pointers to supporting material. While the main text contains the benchmark comparisons (including figures, error analysis, and implementation details for the GaAs case), the abstract should not stand alone in a way that makes evaluation difficult. In the revised version we will update the abstract to state that quantitative agreement is demonstrated in the main text (with explicit reference to the relevant sections and figures) and will qualify the claim to note that it holds within the reported numerical precision and for the specific observables considered. This addresses the load-bearing nature of the statement without expanding the abstract beyond its intended length. revision: yes

Circularity Check

0 steps flagged

No significant circularity; benchmarks are independent

full rationale

The paper derives its quantum simulation framework from standard second-quantization and Brillouin-zone discretization, then directly benchmarks linear absorption and optical gain spectra against independent classical semiconductor Bloch equation simulations for GaAs, reporting quantitative agreement in the noiseless limit. No equations or parameters are fitted inside the paper and then relabeled as predictions; the many-body extension is explicitly scoped as future work without any supporting derivation or self-referential claim. The central results rest on external classical benchmarks rather than internal definitions or self-citations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard quantum mechanics and semiconductor physics; no free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Brillouin-zone discretization accurately represents the semiconductor band structure for optical response calculations
    Invoked as the basis for the simulation framework
  • domain assumption Second-quantization formalism is appropriate for modeling light-matter interactions in the semi-classical regime
    Used to construct the quantum simulation

pith-pipeline@v0.9.1-grok · 5755 in / 1335 out tokens · 24174 ms · 2026-06-28T09:20:05.801567+00:00 · methodology

0 comments
read the original abstract

We present a digital quantum simulation framework for ultrafast optical spectroscopy of semiconductor materials. The framework is based on Brillouin-zone discretization and the second-quantization formalism, and is designed as a quantum alternative to classical simulations based on the semiconductor Bloch equations. Its current capabilities include quantum simulations of linear absorption and optical gain spectra, incorporating Lorentzian broadening, finite-temperature band-filling effects, and reduced-dimensionality effects. Benchmark comparisons with classical simulations for GaAs demonstrate quantitative agreement in the noiseless limit. The inclusion of realistic hardware noise of NISQ-era quantum computers effectively manifests itself as an additional source of scattering processes, resulting in increased spectral broadening. While no exponential quantum advantage is expected in the single-particle approximation, the framework naturally extends to many-body regimes where classical simulations face the hierarchy problem and exponential scaling and provable quantum advantage will be possible. The quantum simulations considered in this work capture central elements of semiconductor spectroscopy, the aspects such as open quantum systems, light-matter interactions, statistical mechanics, non-equilibrium quantum dynamics, and many-body physics. As such, it provides a physically motivated and scalable model for benchmarking quantum computers in applications to complex, real-world problems.

Figures

Figures reproduced from arXiv: 2606.04295 by Bahar Goldozian, Jared H. Cole, Muhammad Usman, Mykhailo Klymenko, Thong Hoang.

Figure 1
Figure 1. Figure 1: FIG. 1. Mapping spectroscopic experiments onto qubit [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum circuit diagram for one Trotter step of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Example quantum circuit for semiconductor time [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of classical (black line) and quantum [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Real (upper row) and imaginary (bottom row) parts [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. omparison of classical (black line) and quantum (blue [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Linear absorption spectra for GaAs obtained using classical simulations (shaded area), noiseless quantum simulations [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Gain spectra of 2D GaAs computed using classical [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 6 canonical work pages · 1 internal anchor

  1. [1]

    Challenges The problem stated in the previous section shows that accurate simulation of ultrafast spectroscopy involves several physical effects that lie beyond the unitary dy- namics native to qubit-based quantum computers, pos- ing the challenge of efficient implementation within quan- tum computing constraints. Another challenge is that spectroscopic a...

  2. [2]

    Discretization of the Brillouin zone The standard discretization approach relies on the Born–von Karman boundary conditions. These condi- tions imply that, instead of treating the semiconductor as an infinite system, one considers a crystal of finite size (defined byntranslations of primitive cell defined by the primitive translation vectorsa j) and appli...

  3. [3]

    (4)–(6)) can be simulated on a quantum computer by imposing the fermionic anti- commutation relations on qubits that obey a tensor- product spin algebra

    Mapping fermionic operators to qubits: Jordan–Wigner transformation The fermionic creation and annihilation operators in- troduced above (see Eqs. (4)–(6)) can be simulated on a quantum computer by imposing the fermionic anti- commutation relations on qubits that obey a tensor- product spin algebra. To simulate fermionic systems on qubits, a fermion-to-qu...

  4. [4]

    (11) - on a quantum computer

    Time evolution and trotterization After discretizing the Brillouin zone and mapping the Hamiltonian to a qubit representation, the problem re- duces to computing time-dependent expectation values - such as the polarization or induced dipole moment in Eq. (11) - on a quantum computer. The expectation val- ues depend on the time evolution of the density mat...

  5. [5]

    At the circuit level, the trajectories are obtained from re- peated circuit executions with variable quantum gates sampled according to a prescribed probability distribu- tion

    by sampling an ensemble of systems undergoing uni- tary dynamics and averaging over their trajectories. At the circuit level, the trajectories are obtained from re- peated circuit executions with variable quantum gates sampled according to a prescribed probability distribu- tion. In the limit of a sufficiently large number of shots, the ensemble-averaged ...

  6. [6]

    Jimenez and J

    J. Jimenez and J. Tomm,Spectroscopic Analysis of Op- toelectronic Semiconductors, Springer Series in Optical Sciences (Springer International Publishing, 2018)

    2018

  7. [7]

    Kalt and C

    H. Kalt and C. Klingshirn,Semiconductor Optics 1: Linear Optical Properties of Semiconductors, Gradu- ate Texts in Physics (Springer International Publishing, 2019)

    2019

  8. [8]

    Chow and S

    W. Chow and S. Koch,Semiconductor-Laser Fundamen- tals: Physics of the Gain Materials(Springer, 1999)

    1999

  9. [9]

    Haug and S

    H. Haug and S. W. Koch,Quantum Theory of the Opti- cal and Electronic Properties of Semiconductors, 5th ed. (World Scientific, 2009)

    2009

  10. [10]

    Piprek,Optoelectronic Devices: Advanced Simula- tion and Analysis, [ProQuest Ebook Central] (Springer, 2005)

    J. Piprek,Optoelectronic Devices: Advanced Simula- tion and Analysis, [ProQuest Ebook Central] (Springer, 2005)

    2005

  11. [11]

    Nisoli,Semiconductor Laser Photonics, 2nd ed

    M. Nisoli,Semiconductor Laser Photonics, 2nd ed. (Cam- bridge University Press, 2022)

    2022

  12. [12]

    L. P. Kadanoff and G. Baym,Quantum Statistical Me- chanics: Green ’s Function Methods in Equilibrium and Nonequilibrium Problems, Frontiers in Physics, Vol. 8 (W. A. Benjamin, New York, 1962)

    1962

  13. [13]

    Stefanucci and R

    G. Stefanucci and R. van Leeuwen,Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction(Cambridge University Press, Cambridge, 2013)

    2013

  14. [14]

    Bonitz,Quantum Kinetic Theory(Springer Interna- tional Publishing, 2016)

    M. Bonitz,Quantum Kinetic Theory(Springer Interna- tional Publishing, 2016)

    2016

  15. [15]

    Kira and S

    M. Kira and S. Koch, Many-body correlations and exci- tonic effects in semiconductor spectroscopy, Progress in Quantum Electronics30, 155 (2006)

    2006

  16. [16]

    R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics21, 467 (1982)

    1982

  17. [17]

    Lloyd, Universal quantum simulators, Science273, 1073 (1996)

    S. Lloyd, Universal quantum simulators, Science273, 1073 (1996)

    1996

  18. [18]

    Bauer, S

    B. Bauer, S. Bravyi, M. Motta, and G. K.-L. Chan, Quantum algorithms for quantum chemistry and quan- tum materials science, Chemical reviews120, 12685 (2020)

    2020

  19. [19]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Quantum computational chemistry, Rev. Mod. Phys.92, 015003 (2020)

    2020

  20. [20]

    Sherbert, A

    K. Sherbert, A. Jayaraj, and M. Buongiorno Nardelli, Quantum algorithm for electronic band structures with local tight-binding orbitals, Scientific Reports12, 9867 (2022)

    2022

  21. [21]

    H. Ma, M. Govoni, and G. Galli, Quantum simulations of materials on near-term quantum computers, npj Com- putational Materials6, 85 (2020)

    2020

  22. [22]

    Watkins, N

    J. Watkins, N. Wiebe, A. Roggero, and D. Lee, Time- dependent hamiltonian simulation using discrete-clock constructions, PRX Quantum5, 040316 (2024)

    2024

  23. [23]

    Zylberman, T

    J. Zylberman, T. Fredon, N. F. Loureiro, and F. Deb- basch, Trotter-based quantum algorithm for solving transport equations with exponentially fewer time-steps, Quantum Science and Technology11, 025015 (2026)

    2026

  24. [24]

    A. N. Chowdhury, G. H. Low, and N. Wiebe, A varia- tional quantum algorithm for preparing quantum gibbs states, arXiv preprint arXiv:2002.00055 (2020)

    work page Pith review arXiv 2002

  25. [25]

    Rajakumar and J

    J. Rajakumar and J. D. Watson, Gibbs sampling gives quantum advantage at constant temperatures with O (1)- local Hamiltonians, Quantum10, 1981 (2026)

    1981

  26. [26]

    C.-F. Chen, M. Kastoryano, F. G. S. L. Brand˜ ao, and A. Gily´ en, Efficient quantum thermal simulation, Nature 646, 561 (2025)

    2025

  27. [27]

    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

  28. [28]

    K. R. Fratus, N. Enenkel, S. Zanker, J.-M. Reiner, M. Marthaler, and P. Schmitteckert, Can a quantum computer simulate nuclear magnetic resonance spectra better than a classical one? (2026), arXiv:2508.06448 [quant-ph]

    work page arXiv 2026

  29. [29]

    Bruschi, F

    M. Bruschi, F. Gallina, and B. Fresch, A quantum algo- rithm from response theory: Digital quantum simulation of two-dimensional electronic spectroscopy, The Journal of Physical Chemistry Letters15, 1484 (2024)

    2024

  30. [30]

    G. D. Mahan,Many-particle physics(Springer Science and Business Media, LLC, 2000)

    2000

  31. [31]

    A. L. Fetter and J. D. Walecka,Quantum theory of many- particle systems(Courier Corporation, 2012)

    2012

  32. [32]

    Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, 2015)

    P. Coleman,Introduction to Many-Body Physics(Cam- bridge University Press, 2015)

    2015

  33. [33]

    Breuer and F

    H.-P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, 2007)

    2007

  34. [34]

    Nakajima, On quantum theory of transport phenom- ena: Steady diffusion, Progress of Theoretical Physics 20, 948 (1958)

    S. Nakajima, On quantum theory of transport phenom- ena: Steady diffusion, Progress of Theoretical Physics 20, 948 (1958)

    1958

  35. [35]

    Zwanzig, Ensemble method in the theory of irre- versibility, The Journal of Chemical Physics33, 1338 (1960)

    R. Zwanzig, Ensemble method in the theory of irre- versibility, The Journal of Chemical Physics33, 1338 (1960)

    1960

  36. [36]

    Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (heom), The Journal of Chemical Physics153, 020901 (2020)

    Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (heom), The Journal of Chemical Physics153, 020901 (2020)

    2020

  37. [37]

    L. H. Delgado-Granados, S. Warren, and D. A. Mazziotti, Unitary dynamics for open quantum sys- tems with density-matrix purification, arXiv preprint arXiv:2406.01783 (2024)

    work page arXiv 2024

  38. [38]

    M. B. Plenio and P. L. Knight, The quantum-jump ap- proach to dissipative dynamics in quantum optics, Rev. Mod. Phys.70, 101 (1998)

    1998

  39. [39]

    Ellmers, A

    C. Ellmers, A. Girndt, M. Hofmann, A. Knorr, W. W. R¨ uhle, F. Jahnke, S. W. Koch, C. Hanke, L. Korte, and C. Hoyler, Measurement and calculation of gain spectra for (GaIn)As/(AlGa)As single quantum well lasers, Ap- plied Physics Letters72, 1647 (1998)

    1998

  40. [40]

    J. M. Booth, M. V. Klymenko, J. H. Cole, and S. P. Russo, Accurate calculation of excitonic signatures in the absorption spectrum of BiSBr using semiconductor Bloch equations, Phys. Rev. B103, 115203 (2021). 15

    2021

  41. [41]

    Klimenko, I

    M. Klimenko, I. Safonov, O. Shulika, and I. Sukhoivanov, Anisotropy of the valence subbands in quantum well structures: effect on density of states characteristic, in NUSOD ’05. Proceedings of the 5th International Confer- ence on Numerical Simulation of Optoelectronic Devices, 2005.(2005) pp. 73–74

    2005

  42. [42]

    Helgaker, P

    T. Helgaker, P. Jorgensen, and J. Olsen,Molecular Electronic-Structure Theory(Wiley, 2013)

    2013

  43. [43]

    R. W. Chien, M. Chiew, B. Harrison, J. Necaise, W. Wang, M. Mudassar, C. McLauchlan, T. M. Henderson, G. E. Scuseria, S. Strelchuk, and J. D. Whitfield, Simulating fermions with a digital quantum computer, Nature Reviews Physics 10.1038/s42254-025- 00914-5 (2026)

    work page doi:10.1038/s42254-025- 2026

  44. [44]

    Y.-A. Chen, A. V. Gorshkov, and Y. Xu, Error-correcting codes for fermionic quantum simulation, SciPost Physics 16, 033 (2024)

    2024

  45. [45]

    Miller, Aaron and Zimbor´ as, Zolt´ an and Knecht, Stefan and Maniscalco, Sabrina and Garc´ ıa-P´ erez, Guillermo, Bonsai algorithm: Grow your own fermion-to-qubit map- pings, PRX quantum4, 030314 (2023)

    2023

  46. [46]

    Li, H.-Y

    Q.-S. Li, H.-Y. Liu, Q. Wang, Y.-C. Wu, and G.-P. Guo, A unified framework of transformations based on the jordan–wigner transformation, The Journal of Chemical Physics157(2022)

    2022

  47. [47]

    Whitfield, James D and Biamonte, Jacob and Aspuru- Guzik, Al´ an, Simulation of electronic structure hamilto- nians using quantum computers, Molecular Physics109, 735 (2011)

    2011

  48. [48]

    M. A. Nielsenet al., The fermionic canonical commuta- tion relations and the jordan-wigner transform, School of Physical Sciences The University of Queensland59, 75 (2005)

    2005

  49. [49]

    Somma, G

    R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Simulating physical phenomena by quan- tum networks, Physical Review A65, 042323 (2002)

    2002

  50. [50]

    J. T. Seeley, M. J. Richard, and P. J. Love, The Bravyi- Kitaev transformation for quantum computation of elec- tronic structure, The Journal of chemical physics137 (2012)

    2012

  51. [52]

    Jordan and E

    P. Jordan and E. P. Wigner, About the pauli exclusion principle, Z. Phys47, 14 (1928)

    1928

  52. [53]

    S. B. Bravyi and A. Y. Kitaev, Fermionic quantum com- putation, Annals of Physics298, 210 (2002)

    2002

  53. [54]

    V. c. v. Havl´ ıˇ cek, M. Troyer, and J. D. Whitfield, Op- erator locality in the quantum simulation of fermionic models, Phys. Rev. A95, 032332 (2017)

    2017

  54. [55]

    Derby, J

    C. Derby, J. Klassen, J. Bausch, and T. Cubitt, Compact fermion to qubit mappings, Phys. Rev. B104, 035118 (2021)

    2021

  55. [56]

    Clinton, J

    L. Clinton, J. Bausch, and T. Cubitt, Hamiltonian simu- lation algorithms for near-term quantum hardware, Na- ture Communications12, 4989 (2021)

    2021

  56. [57]

    P. Zeng, J. Sun, L. Jiang, and Q. Zhao, Simple and high- precision hamiltonian simulation by compensating trot- ter error with linear combination of unitary operations, PRX Quantum6, 010359 (2025)

    2025

  57. [58]

    G. H. Low and I. L. Chuang, Optimal hamiltonian sim- ulation by quantum signal processing, Phys. Rev. Lett. 118, 010501 (2017)

    2017

  58. [59]

    Motlagh and N

    D. Motlagh and N. Wiebe, Generalized quantum signal processing, PRX Quantum5, 020368 (2024)

    2024

  59. [60]

    D. W. Berry, D. Motlagh, G. Pantaleoni, and N. Wiebe, Doubling the efficiency of hamiltonian simulation via gen- eralized quantum signal processing, Phys. Rev. A110, 012612 (2024)

    2024

  60. [61]

    G. H. Low and I. L. Chuang, Hamiltonian simulation by qubitization, Quantum3, 163 (2019)

    2019

  61. [62]

    Poulin, A

    D. Poulin, A. Qarry, R. Somma, and F. Verstraete, Quan- tum simulation of time-dependent hamiltonians and the convenient illusion of hilbert space, Phys. Rev. Lett.106, 170501 (2011)

    2011

  62. [63]

    M. Suzuki, Decomposition formulas of exponential op- erators and lie exponentials with some applications to quantum mechanics and statistical physics, Journal of mathematical physics26, 601 (1985)

    1985

  63. [64]

    P. K. Faehrmann, J. Eisert, and R. Kueng, In the shadow of the hadamard test: Using the garbage state for good and further modifications, Phys. Rev. Lett.135, 150603 (2025)

    2025

  64. [65]

    A. W. Schlimgen, K. Head-Marsden, L. M. Sager-Smith, P. Narang, and D. A. Mazziotti, Quantum simulation of open quantum systems using density-matrix purification, arXiv preprint arXiv:2207.07112 (2022)

    work page arXiv 2022

  65. [66]

    H.-B. Chen, C. Gneiting, P.-Y. Lo, Y.-N. Chen, and F. Nori, Simulating open quantum systems with hamilto- nian ensembles and the nonclassicality of the dynamics, Phys. Rev. Lett.120, 030403 (2018)

    2018

  66. [67]

    Chen, P.-Y

    H.-B. Chen, P.-Y. Lo, C. Gneiting, J. Bae, Y.-N. Chen, and F. Nori, Quantifying the nonclassicality of pure de- phasing, Nature Communications10, 3794 (2019)

    2019

  67. [68]

    Ollivier and W

    H. Ollivier and W. H. Zurek, Quantum discord: A mea- sure of the quantumness of correlations, Phys. Rev. Lett. 88, 017901 (2001)

    2001

  68. [69]

    De Checchi, F

    P. De Checchi, F. Gallina, B. Fresch, and G. G. Gius- teri, On the noisy road to open quantum dynamics: The place of stochastic hamiltonians, Annalen der Physik 538, e00482 (2026)

    2026

  69. [70]

    De Checchi, F

    P. De Checchi, F. Gallina, B. Fresch, and G. G. Gius- teri, Quantum trajectories and reduced dynamics in time-correlated environments, The Journal of Chemical Physics164, 164103 (2026)

    2026

  70. [71]

    D. W. Berry, A. M. Childs, A. Ostrander, and G. Wang, Quantum algorithm for linear differential equations with exponentially improved dependence on precision, Com- munications in Mathematical Physics356, 1057 (2017)

    2017

  71. [72]

    Kanno, I

    S. Kanno, I. Hamamura, R. Raymond, Q. Gao, and N. Yamamoto, Efficient Implementation of Random- ized Quantum Algorithms With Dynamic Circuits , IEEE Transactions on Quantum Engineering7, 1 (2026)

    2026

  72. [73]

    Babbush, D

    R. Babbush, D. W. Berry, R. Kothari, R. D. Somma, and N. Wiebe, Exponential quantum speedup in simulat- ing coupled classical oscillators, Phys. Rev. X13, 041041 (2023)

    2023

  73. [74]

    J. A. Acebr´ on, L. L. Bonilla, C. J. P´ erez Vicente, F. Ri- tort, and R. Spigler, The kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys.77, 137 (2005)

    2005

  74. [75]

    C. M. G. Leditto, A. Southwell, M. Usman, and K. Modi, Efficient quantum algorithms for higher-order coupled os- cillators (2026), arXiv:2604.20108 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026