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arxiv: 2605.05479 · v1 · submitted 2026-05-06 · 🪐 quant-ph · hep-ph

Recognition: unknown

Quantum Simulation of the Real-time Dynamics in the multi-flavor Gross-Neveu Model at the utility scale using Superconducting Quantum Computers

Talal Ahmed Chowdhury , Seokwon Choi , Kyoungchul Kong , Kwangmin Yu
Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:09 UTC · model grok-4.3

classification 🪐 quant-ph hep-ph
keywords quantum simulationGross-Neveu modelTrotterizationsuperconducting qubitsreal-time dynamicsfermionic field theorydiagonal operator approximationutility-scale quantum computing
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The pith

A controlled approximation for diagonal operators lets superconducting quantum processors simulate real-time dynamics of the multi-flavor Gross-Neveu model beyond 100 qubits.

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

The authors construct a Trotterized simulation of the 1+1 dimensional multi-flavor Gross-Neveu model whose circuit depth grows with the number of flavors rather than total lattice size. They introduce the Localized Diagonal Operator Approximation to replace the costly implementation of quartic interaction terms with an analytic least-squares reconstruction of the required diagonal unitary. The resulting error is shown to vanish in the small-step limit, providing a mathematically controlled reduction in two-qubit gate count. Large-scale runs on IBM superconducting hardware produce density-density correlators that match exact diagonalization and tensor-network references across tested system sizes. The work therefore supplies both a concrete method and a scaling pathway for near-term quantum simulation of interacting fermionic theories.

Core claim

The Localized Diagonal Operator Approximation formulates the synthesis of each diagonal unitary arising from quartic interactions as a structured least-squares problem in phase space whose solution is obtained via the Moore-Penrose pseudoinverse; the unitary error is thereby directly tied to the phase-reconstruction residual and vanishes asymptotically as the Trotter step size is reduced. When combined with a hardware-efficient Trotterization whose depth scales only with flavor number, this approximation reduces two-qubit gate counts enough to enable simulations on more than 100 qubits while preserving quantitative agreement with classical benchmarks for real-time observables.

What carries the argument

Localized Diagonal Operator Approximation (LDOA), which replaces exact diagonal unitaries for long-range quartic terms by an analytic phase-space least-squares solution that lowers circuit depth on limited-connectivity hardware.

If this is right

  • Simulations of the multi-flavor Gross-Neveu model become feasible on current superconducting processors at system sizes exceeding 100 qubits.
  • Real-time observables such as density-density correlators can be extracted with quantitative agreement to classical methods.
  • The same diagonal-operator technique applies to any model whose interaction terms produce long-range diagonal unitaries on hardware with restricted connectivity.
  • Circuit-depth scaling linear in flavor number rather than total size supplies a concrete route toward larger or higher-dimensional fermionic field theories.

Where Pith is reading between the lines

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

  • The same least-squares phase reconstruction could be applied to other lattice models whose Hamiltonians contain similar quartic or long-range diagonal pieces.
  • Error bounds derived from the pseudoinverse residual may be used to select optimal Trotter steps without exhaustive numerical testing.
  • If the method extends to two spatial dimensions, it would open direct quantum simulation of phase structure in theories that remain difficult for classical tensor networks.

Load-bearing premise

The phase-space least-squares reconstruction of each diagonal unitary remains sufficiently accurate that the accumulated Trotter error stays controlled for the chosen step sizes and lattice sizes.

What would settle it

If successively smaller Trotter steps produce density-density correlators that diverge from exact-diagonalization or tensor-network results rather than converging to them, the controlled accuracy of the LDOA would be falsified.

Figures

Figures reproduced from arXiv: 2605.05479 by Kwangmin Yu, Kyoungchul Kong, Seokwon Choi, Talal Ahmed Chowdhury.

Figure 1
Figure 1. Figure 1: FIG. 1: The single Trotter-step of the first-order Trotterization circuit highlighting the consecutive fermionic lattice view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The quantum circuit of the corresponding unitary operator associated with the quartic interaction term acting view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The quantum circuit of the corresponding unitary operator associated with the quartic interaction term acting view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The quantum circuit of the corresponding unitary operator associated with the quartic interaction term acting view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Target circuit for the diagonal operator approximation for the 2-flavor model. The circuit is constructed from view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Comparison of three 4-qubit circuits. (a) CP-based approximation Ansatz circuit obtained by applying the view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Geometric interpretation of a least squares problem. The target vector view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Comparison of the theoretical landscapes of the CP and RZZ Ansatze as a function of view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The diagonal part approximation of the quartic part of the 2-flavor implementation. view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Target circuit for the diagonal operator approximation of the 3-flavor model. The circuit is constructed from view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Comparison of the two 6-qubit circuits. (a) CP-based Ansatz circuit obtained by applying the Diagonal view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Target circuit for the diagonal operator approximation of the 4-flavor model. The circuit is constructed from view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Comparison of the two 8-qubit circuits. (a) CP-based Ansatz circuit obtained by applying the Diagonal view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Comparison of CZ gate depth and CZ gate count between the original circuit and the LDOA-optimized view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: The time evolution of the density-density correlation in the two-flavor Gross-Neveu model with view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: The time evolution of the density-density correlation in the two-flavor Gross-Neveu model with view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: The quantum circuit associated with the randomized measurement (RM) protocol. Here, the local view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: The second R´enyi entropy, view at source ↗
read the original abstract

We present a scalable quantum simulation framework for real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions. Using superconducting quantum processors at utility scale, we develop a hardware-efficient Trotterization whose per-step circuit depth scales with fermion flavor number rather than total system size, enabling simulations beyond 100 qubits. A central contribution of this work is the Localized Diagonal Operator Approximation (LDOA), which systematically reduces the overhead associated with quartic interactions. We formulate diagonal unitary synthesis as a structured least-squares problem in phase space and obtain analytic solutions via the Moore-Penrose pseudoinverse. This formulation provides a principled and quantitatively controlled approximation: in the small Trotter-step regime, the unitary error is directly linked to the phase reconstruction error and vanishes asymptotically as the Trotter step size decreases. This establishes a clear mathematical foundation for the LDOA while significantly reducing two-qubit gate counts and circuit depth, and is broadly applicable to diagonal quantum operators with long-range structure, making it particularly well suited for quantum hardware with limited qubit connectivity. Using these techniques, we run large-scale simulations on IBM superconducting processors and study real-time observables, including density-density correlators. We benchmark against exact diagonalization and tensor network-based methods, finding strong agreement across system sizes. These results show that combining hardware-aware circuit design with rigorous approximations enables practical near-term simulation of interacting fermionic field theories and provides a scalable pathway toward more complex quantum field theory simulations.

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

2 major / 2 minor

Summary. The manuscript presents a scalable quantum simulation framework for the real-time dynamics of the multi-flavor Gross-Neveu model in 1+1 dimensions on superconducting quantum processors at utility scale (>100 qubits). It develops a hardware-efficient Trotterization whose depth scales with flavor number, and introduces the Localized Diagonal Operator Approximation (LDOA) that reduces quartic interaction overhead by formulating diagonal unitary synthesis as a structured least-squares problem in phase space solved via the Moore-Penrose pseudoinverse. The authors claim this yields a controlled approximation where unitary error is proportional to phase reconstruction error and vanishes asymptotically for small Trotter steps. They simulate density-density correlators and report strong agreement with exact diagonalization and tensor-network benchmarks.

Significance. If the LDOA error remains quantitatively controlled for the quartic operators and system sizes actually run on hardware, and if the reported benchmark agreement extends reliably beyond small-system validation, the work demonstrates a practical route to near-term simulation of interacting fermionic field theories. The combination of hardware-aware circuit design, analytic least-squares error bounds, and explicit scaling of circuit depth with flavor number rather than total size constitutes a concrete advance over generic Trotterization approaches for long-range diagonal operators.

major comments (2)
  1. [LDOA formulation and error analysis] The central claim that the LDOA provides a 'principally and quantitatively controlled approximation' whose unitary error 'vanishes asymptotically as the Trotter step size decreases' (abstract) is load-bearing for the scalability argument. However, the manuscript does not appear to supply explicit numerical verification of this scaling for the concrete quartic interaction terms, the specific flavor numbers, and the finite Trotter steps employed in the >100-qubit hardware runs. The conditioning of the phase-space sampling matrix and the residual norm of the Moore-Penrose solution should be reported to confirm that reconstruction error does not introduce systematic bias in the real-time evolution of density-density correlators.
  2. [Results and benchmarking] The abstract states 'strong agreement' with exact diagonalization and tensor-network benchmarks 'across system sizes,' yet provides no quantitative error metrics (e.g., maximum deviation in correlators, fidelity per Trotter step, or dependence on system size). Without these, it is impossible to assess whether the agreement supports extrapolation to the utility-scale regime where the LDOA is most needed.
minor comments (2)
  1. The abstract would be strengthened by including at least one concrete quantitative result (e.g., largest system size simulated, number of Trotter steps, or observed correlator error relative to benchmarks).
  2. Notation for the phase-space least-squares problem and the definition of the Localized Diagonal Operator Approximation should be introduced with an explicit equation number on first use to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The two major comments identify areas where additional numerical evidence and quantitative metrics will strengthen the manuscript. We address each point below and will incorporate the requested material in a revised version.

read point-by-point responses

  1. Referee: [LDOA formulation and error analysis] The central claim that the LDOA provides a 'principally and quantitatively controlled approximation' whose unitary error 'vanishes asymptotically as the Trotter step size decreases' (abstract) is load-bearing for the scalability argument. However, the manuscript does not appear to supply explicit numerical verification of this scaling for the concrete quartic interaction terms, the specific flavor numbers, and the finite Trotter steps employed in the >100-qubit hardware runs. The conditioning of the phase-space sampling matrix and the residual norm of the Moore-Penrose solution should be reported to confirm that reconstruction error does not introduce systematic bias in the real-time evolution of density-density correlators.

    Authors: We appreciate the referee's emphasis on explicit verification. The manuscript derives the controlled nature of the LDOA analytically by showing that the unitary error is bounded by the phase-reconstruction residual of the Moore-Penrose solution and therefore vanishes as the Trotter step size decreases. To supply the requested numerical confirmation for the quartic operators, specific flavor numbers, and the finite steps used in the hardware runs, we will add a dedicated subsection containing (i) plots of unitary error versus Trotter step size, (ii) the condition numbers of the phase-space sampling matrices, and (iii) the residual norms of the pseudoinverse solutions. These additions will demonstrate that reconstruction error remains small and does not introduce measurable bias in the reported correlators. revision: yes

  2. Referee: [Results and benchmarking] The abstract states 'strong agreement' with exact diagonalization and tensor-network benchmarks 'across system sizes,' yet provides no quantitative error metrics (e.g., maximum deviation in correlators, fidelity per Trotter step, or dependence on system size). Without these, it is impossible to assess whether the agreement supports extrapolation to the utility-scale regime where the LDOA is most needed.

    Authors: We agree that quantitative metrics are necessary for a rigorous assessment. In the revised manuscript we will augment the benchmarking section with explicit error measures: maximum and mean absolute deviations of the density-density correlators, average fidelity per Trotter step, and their dependence on system size and flavor number. These quantities will be reported separately for the exact-diagonalization comparisons (small systems) and the tensor-network comparisons (larger systems), thereby providing the quantitative basis for the claim of strong agreement and for extrapolation to the utility-scale regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity in LDOA derivation or simulation framework

full rationale

The paper derives the Localized Diagonal Operator Approximation (LDOA) explicitly as a structured least-squares problem in phase space solved via the Moore-Penrose pseudoinverse, with the unitary error bound stated to be directly proportional to phase reconstruction error and to vanish asymptotically for small Trotter steps. This is a self-contained mathematical construction whose error scaling is tied to the step size by definition of the approximation, not to any fitted parameters, self-citations, or prior results from the same authors. No load-bearing steps reduce to self-definition, renamed known results, or imported uniqueness theorems; external benchmarks against exact diagonalization and tensor networks are invoked for validation rather than as internal justification. The overall framework (hardware-efficient Trotterization plus LDOA) therefore remains independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are detailed. The LDOA is presented as a new approximation technique rather than an invented physical entity.

pith-pipeline@v0.9.0 · 5586 in / 1209 out tokens · 55802 ms · 2026-05-08T16:09:52.451043+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

80 extracted references · 52 canonical work pages

  1. [1]

    The quartic terms are composed of single-qubit phase gates, two-qubit phase gates (CP gates), and SWAP gates

    This design requires 4( N− 1) SWAP-gate layers for the N- flavor system. The quartic terms are composed of single-qubit phase gates, two-qubit phase gates (CP gates), and SWAP gates. Since the main challenge in implementing the quartic term is the two-qubit phase gate, we focus on its implementation. Figure 5 shows the two-qubit phase gate and the SWAP ga...

  2. [2]

    In the form, the target unitary is diagonal in the computational basis as shown Fig

    2-flavor Model We apply the diagonal operator approximation to the two-flavor Gross–Neveu evolution operator restricted to a fixed fermion-number sector. In the form, the target unitary is diagonal in the computational basis as shown Fig. 5 and can be written as Utarget(⃗ϕ(θg)) = diag 1,1,1, e iθg ,1, e −iθg , e−iθg , e−iθg ,1, e −iθg , e−iθg , e−iθg , ei...

  3. [3]

    In the form, the target unitary operator and the Ansatz unitary operators are visualized in Fig

    3-flavor Model We apply the diagonal operator approximation to the three-flavor Gross–Neveu evolution operator restricted to a fixed fermion-number sector. In the form, the target unitary operator and the Ansatz unitary operators are visualized in Fig. 10 and 11, respectively. 14 q0 • P(− θg 6 )q1 • • P(− 13θg 12 )q2 • P(− θg 6 ) • q3 • (a) CP-based appro...

  4. [4]

    In the form, the target unitary operator and the Ansatz unitary operators are visualized in Fig

    4-flavor Model In this example, we apply the diagonal operator approximation to the four-flavor Gross–Neveu evolution operator restricted to a fixed fermion-number sector. In the form, the target unitary operator and the Ansatz unitary operators are visualized in Fig. 12 and 13, respectively. q2n,0 : • P(θ g) • P(θ g) × • P(−θ g) × • P(θ g) × × × × q2n,1 ...

    1968

  5. [5]

    R. J. Lewis-Swan, A. Safavi-Naini, A. M. Kaufman, and A. M. Rey, Dynamics of quantum information, Nature Reviews Physics1, 627 (2019), arXiv:1908.11747 [quant-ph]

    work page arXiv 2019

  6. [6]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum Simulation, Rev. Mod. Phys.86, 153 (2014), arXiv:1308.6253 [quant-ph]

    work page arXiv 2014

  7. [7]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quantum simulation, Nature607, 667 (2022)

    2022

  8. [8]

    Simulating lattice gauge theories on a quantum computer

    T. Byrnes and Y. Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys. Rev. A73, 022328 (2006), arXiv:quant-ph/0510027 [quant-ph]

    work page Pith review arXiv 2006

  9. [9]

    S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum Algorithms for Quantum Field Theories, Science336, 1130 (2012), arXiv:1111.3633 [quant-ph]

    work page Pith review arXiv 2012

  10. [10]

    S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum Computation of Scattering in Scalar Quantum Field Theories, arXiv e-prints , arXiv:1112.4833 (2011), arXiv:1112.4833 [hep-th]

    work page Pith review arXiv 2011

  11. [11]

    S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum Algorithms for Fermionic Quantum Field Theories, arXiv e-prints , arXiv:1404.7115 (2014), arXiv:1404.7115 [hep-th]

    work page Pith review arXiv 2014

  12. [12]

    S. P. Jordan, H. Krovi, K. S. M. Lee, and J. Preskill, BQP-completeness of scattering in scalar quantum field theory, Quantum2, 44 (2018), arXiv:1703.00454 [quant-ph]

    work page arXiv 2018

  13. [13]

    D. J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D10, 3235 (1974)

    1974

  14. [14]

    R. F. Dashen, B. Hasslacher, and A. Neveu, Semiclassical bound states in an asymptotically free theory, Phys. Rev. D12, 2443 (1975)

    1975

  15. [15]

    elementary

    A. B. Zamolodchikov and A. B. Zamolodchikov, Exact S matrix of Gross-Neveu “elementary” fermions, Physics Letters B 72, 481 (1978)

    1978

  16. [16]

    A. B. Zamolodchikov and A. B. Zamolodchikov, Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models, Annals Phys.120, 253 (1979)

    1979

  17. [17]

    Witten, Some Properties of the (psi-Bar psi)**2 Model in Two-Dimensions, Nucl

    E. Witten, Some Properties of the (psi-Bar psi)**2 Model in Two-Dimensions, Nucl. Phys. B142, 285 (1978)

    1978

  18. [18]

    Thies and K

    M. Thies and K. Urlichs, Revised phase diagram of the Gross-Neveu model, Phys. Rev. D67, 125015 (2003), arXiv:hep- th/0302092 [hep-th]

    work page arXiv 2003

  19. [19]

    Schnetz, M

    O. Schnetz, M. Thies, and K. Urlichs, Phase diagram of the Gross Neveu model: exact results and condensed matter precursors, Annals of Physics314, 425 (2004), arXiv:hep-th/0402014 [hep-th]

    work page arXiv 2004

  20. [20]

    J. Lenz, L. Pannullo, M. Wagner, B. Wellegehausen, and A. Wipf, Inhomogeneous phases in the Gross-Neveu model in 1 +1 dimensions at finite number of flavors, Phys. Rev. D101, 094512 (2020), arXiv:2004.00295 [hep-lat]

    work page arXiv 2020

  21. [21]

    J. J. Lenz, L. Pannullo, M. Wagner, B. H. Wellegehausen, and A. Wipf, Baryons in the Gross-Neveu model in 1 +1 dimensions at finite number of flavors, Phys. Rev. D102, 114501 (2020), arXiv:2007.08382 [hep-lat]

    work page arXiv 2020

  22. [22]

    Lajer, R

    M. Lajer, R. M. Konik, R. D. Pisarski, and A. M. Tsvelik, When cold, dense quarks in 1 +1 and 3 +1 dimensions are not a Fermi liquid, Phys. Rev. D105, 054035 (2022), arXiv:2112.10238 [hep-th]

    work page arXiv 2022

  23. [23]

    Ortiz, J

    G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Quantum algorithms for fermionic simulations, Phys. Rev. A64, 022319 (2001), arXiv:cond-mat/0012334 [cond-mat]

    work page arXiv 2001

  24. [24]

    Asaduzzaman, G

    M. Asaduzzaman, G. C. Toga, S. Catterall, Y. Meurice, and R. Sakai, Quantum simulation of the N -flavor Gross-Neveu model, Phys. Rev. D106, 114515 (2022), arXiv:2208.05906 [hep-lat]

    work page arXiv 2022

  25. [25]

    Kogut and L

    J. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D11, 395 (1975)

    1975

  26. [26]

    Banks, L

    T. Banks, L. Susskind, and J. Kogut, Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises, Phys. Rev. D13, 1043 (1976)

    1976

  27. [27]

    Susskind, Lattice fermions, Phys

    L. Susskind, Lattice fermions, Phys. Rev. D16, 3031 (1977)

    1977

  28. [28]

    Roose, N

    G. Roose, N. Bultinck, L. Vanderstraeten, F. Verstraete, K. Van Acoleyen, and J. Haegeman, Lattice regularisation and entanglement structure of the Gross-Neveu model, Journal of High Energy Physics2021, 207 (2021), arXiv:2010.03441 [hep-lat]

    work page arXiv 2021

  29. [29]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das Paulische ¨Aquivalenzverbot, Zeitschrift f¨ ur Physik47, 631 (1928)

    1928

  30. [30]

    Oshikawa and I

    M. Oshikawa and I. Affleck, Field-Induced Gap in S = 1/2 Antiferromagnetic Chains, Phys. Rev. Lett.79, 2883 (1997), arXiv:cond-mat/9706085 [cond-mat.str-el]

    work page arXiv 1997

  31. [31]

    Derzhko and T

    O. Derzhko and T. Verkholyak, Effects of dzyaloshinskii-moriya interaction in the dynamics of s= 1/2 xx chain, Czechoslovak Journal of Physics54, 531 (2004)

    2004

  32. [32]

    H. F. Trotter, On the product of semi-groups of operators, Proceedings of the American Mathematical Society10, 545 (1959)

    1959

  33. [33]

    M. Suzuki, Generalized trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems, Communications in Mathematical Physics51, 183 (1976)

    1976

  34. [34]

    Suzuki, On the convergence of exponential operators-the zassenhaus formula, bch formula and systematic approximants, Communications in Mathematical Physics57, 193 (1977)

    M. Suzuki, On the convergence of exponential operators-the zassenhaus formula, bch formula and systematic approximants, Communications in Mathematical Physics57, 193 (1977). 25

    1977

  35. [35]

    T. A. Chowdhury, K. Yu, M. A. Shamim, M. L. Kabir, and R. S. Sufian, Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers, Physical Review Research6, 033107 (2024), arXiv:2312.12427 [quant-ph]

    work page arXiv 2024

  36. [36]

    T. A. Chowdhury, V. Korepin, V. R. Pascuzzi, and K. Yu, Quantum utility in simulating the real-time dynamics of the Fermi- Hubbard model using superconducting quantum computers, Applied Physics Reviews13, 011434 (2026), arXiv:2509.14196 [quant-ph]

    work page arXiv 2026

  37. [37]

    Y. Chai, A. Crippa, K. Jansen, S. K¨ uhn, V. R. Pascuzzi, F. Tacchino, and I. Tavernelli, Fermionic wave packet scattering: a quantum computing approach, Quantum9, 1638 (2025), arXiv:2312.02272 [quant-ph]

    work page arXiv 2025

  38. [38]

    Layden, First-Order Trotter Error from a Second-Order Perspective, Phys

    D. Layden, First-Order Trotter Error from a Second-Order Perspective, Phys. Rev. Lett.128, 210501 (2022), arXiv:2107.08032 [quant-ph]

    work page arXiv 2022

  39. [39]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information , 10th ed. (Cambridge University Press, 2010)

    2010

  40. [40]

    Ben-Israel and T

    A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed. (Springer New York, 2003)

    2003

  41. [41]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algorithms, Nature Reviews Physics3, 625 (2021), arXiv:2012.09265 [quant-ph]

    work page arXiv 2021

  42. [42]

    Elementary gates for quantum computation

    A. Barenco, C. H. Bennett, R. Cleve, D. P. Divincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Elementary gates for quantum computation, Phys. Rev. A52, 3457 (1995), arXiv:quant-ph/9503016 [quant-ph]

    work page arXiv 1995

  43. [43]

    Muthukrishnan and C

    A. Muthukrishnan and C. R. Stroud, Jr., Multivalued logic gates for quantum computation, Phys. Rev. A62, 052309 (2000), arXiv:quant-ph/0002033 [quant-ph]

    work page arXiv 2000

  44. [44]

    Zhang, K

    K. Zhang, K. Yu, K. Hao, and V. Korepin, Optimal realization of yang–baxter gate on quantum computers, Advanced Quantum Technologies7, 2300345 (2024)

    2024

  45. [45]

    Weinberg and M

    P. Weinberg and M. Bukov, QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems part I: spin chains, SciPost Phys.2, 003 (2017)

    2017

  46. [46]

    M. S. Anis et al., Qiskit: An open-source framework for quantum computing (2021)

    2021

  47. [47]

    Haegeman, J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Verschelde, and F. Verstraete, Time-Dependent Variational Principle for Quantum Lattices, Phys. Rev. Lett.107, 070601 (2011), arXiv:1103.0936 [cond-mat.str-el]

    work page arXiv 2011

  48. [48]

    & Verstraete, F

    J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, Unifying time evolution and optimization with matrix product states, Physical Review B94, 10.1103/physrevb.94.165116 (2016)

    work page doi:10.1103/physrevb.94.165116 2016

  49. [49]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calculations, SciPost Phys. Codebases , 4 (2022)

    2022

  50. [50]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, Codebase release 0.3 for ITensor, SciPost Phys. Codebases , 4 (2022)

    2022

  51. [51]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of Modern Physics81, 865 (2009), arXiv:quant-ph/0702225 [quant-ph]

    work page arXiv 2009

  52. [52]

    Probing entanglement entropy via randomized measurements

    T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing R´ enyi entanglement entropy via randomized measurements, Science364, 260 (2019), arXiv:1806.05747 [quant-ph]

    work page Pith review arXiv 2019

  53. [53]

    S. J. van Enk and C. W. J. Beenakker, Measuring Trρn on single copies of ρ using random measurements, Phys. Rev. Lett. 108, 110503 (2012), arXiv:1112.1027 [quant-ph]

    work page arXiv 2012

  54. [54]

    Elben, B

    A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, R´ enyi Entropies from Random Quenches in Atomic Hubbard and Spin Models, Phys. Rev. Lett.120, 050406 (2018), arXiv:1709.05060 [quant-ph]

    work page arXiv 2018

  55. [55]

    Vermersch, A

    B. Vermersch, A. Elben, M. Dalmonte, J. I. Cirac, and P. Zoller, Unitary n -designs via random quenches in atomic Hubbard and spin models: Application to the measurement of R´ enyi entropies, Phys. Rev. A97, 023604 (2018), arXiv:1801.00999 [quant-ph]

    work page arXiv 2018

  56. [56]

    Elben, B

    A. Elben, B. Vermersch, C. F. Roos, and P. Zoller, Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states, Phys. Rev. A99, 052323 (2019), arXiv:1812.02624 [quant-ph]

    work page arXiv 2019

  57. [57]

    A. Rath, R. van Bijnen, A. Elben, P. Zoller, and B. Vermersch, Importance Sampling of Randomized Measurements for Probing Entanglement, Phys. Rev. Lett.127, 200503 (2021), arXiv:2102.13524 [quant-ph]

    work page arXiv 2021

  58. [58]

    Elben, S

    A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The randomized measurement toolbox, Nature Reviews Physics5, 9 (2023), arXiv:2203.11374 [quant-ph]

    work page arXiv 2023

  59. [59]

    G. Park, K. Zhang, K. Yu, and V. Korepin, Quantum multi-programming for Grover’s search, Quantum Information Processing22, 54 (2023), arXiv:2207.14464 [quant-ph]

    work page arXiv 2023

  60. [60]

    P. Rao, S. Choi, and K. Yu, Quantum multi-programming for maximum likelihood amplitude estimation, Proc. SPIE Int. Soc. Opt. Eng.12911, 129110E (2024)

    2024

  61. [61]

    J. S. Baker, G. Park, K. Yu, A. Ghukasyan, O. Goktas, and S. K. Radha, Parallel hybrid quantum-classical machine learning for kernelized time-series classification, Quantum Machine Intelligence6, 18 (2024), arXiv:2305.05881 [quant-ph]

    work page arXiv 2024

  62. [62]

    T. A. Chowdhury, K. Yu, M. Asaduzzaman, and R. S. Sufian, Capturing the Page curve and entanglement dynamics of black holes in quantum computers, Nuclear Physics B1019, 117112 (2025), arXiv:2412.15180 [quant-ph]

    work page arXiv 2025

  63. [63]

    T. A. Chowdhury, K. Yu, and R. S. Sufian, Probing entanglement dynamics in the SYK model using quantum computers, Results in Physics79, 108526 (2025), arXiv:2503.18580 [quant-ph]

    work page arXiv 2025

  64. [64]

    S. Choi, T. A. Chowdhury, and K. Yu, Quantum utility-scale error mitigation for quantum quench dynamics in Heisenberg spin chains, Physica Scripta101, 035103 (2026), arXiv:2506.20125 [quant-ph]

    work page arXiv 2026

  65. [65]

    arXiv preprint arXiv:2112.07091 , year =

    Y. Ohkura, T. Satoh, and R. Van Meter, Simultaneous Execution of Quantum Circuits on Current and Near-Future NISQ Systems, IEEE Transactions on Quantum Engineering3, TQE.2022 (2022), arXiv:2112.07091 [quant-ph]

    work page arXiv 2022

  66. [66]

    I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, 26 H. Neven, and R. Babbush, Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization, Quantum4, 296 (2020), arXiv:1902.10673 [quant-ph]

    work page arXiv 2020

  67. [67]

    J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction, PRX Quantum2, 030305 (2021), arXiv:2011.03494 [quant- ph]

    work page arXiv 2021

  68. [68]

    Y. Kim, C. J. Wood, T. J. Yoder, S. T. Merkel, J. M. Gambetta, K. Temme, and A. Kandala, Scalable error mitigation for noisy quantum circuits produces competitive expectation values, Nature Phys.19, 752 (2023), arXiv:2108.09197 [quant-ph]

    work page arXiv 2023

  69. [69]

    Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing before fault tolerance, Nature618, 500 (2023)

    2023

  70. [70]

    Charles, E

    C. Charles, E. J. Gustafson, E. Hardt, F. Herren, N. Hogan, H. Lamm, S. Starecheski, R. S. Van de Water, and M. L. Wagman, SimulatingZ 2 lattice gauge theory on a quantum computer, arXiv:2305.02361 [hep-lat]

    work page arXiv

  71. [71]

    van den Berg, Z

    E. van den Berg, Z. K. Minev, and K. Temme, Model-free readout-error mitigation for quantum expectation values, Phys. Rev. A105, 032620 (2022)

    2022

  72. [72]

    Dynamical Decoupling of Open Quantum Systems

    L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett.82, 2417 (1999), arXiv:quant-ph/9809071

    work page Pith review arXiv 1999

  73. [73]

    Ezzell, B

    N. Ezzell, B. Pokharel, L. Tewala, G. Quiroz, and D. A. Lidar, Dynamical decoupling for superconducting qubits: A performance survey, Phys. Rev. Applied20, 064027 (2023), arXiv:2207.03670 [quant-ph]

    work page arXiv 2023

  74. [74]

    Niu and A

    S. Niu and A. Todri-Sanial, Effects of Dynamical Decoupling and Pulse-Level Optimizations on IBM Quantum Computers, IEEE Trans. Quantum Eng.3, 1 (2022), arXiv:2204.01471 [quant-ph]

    work page arXiv 2022

  75. [75]

    C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett.76, 722 (1996), arXiv:quant-ph/9511027 [quant-ph]

    work page arXiv 1996

  76. [76]

    J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Phys. Rev. A 94, 052325 (2016), arXiv:1512.01098 [quant-ph]

    work page arXiv 2016

  77. [77]

    Cai and S

    Z. Cai and S. C. Benjamin, Constructing smaller pauli twirling sets for arbitrary error channels, Scientific Reports9, 10.1038/s41598-019-46722-7 (2019), arXiv:1807.04973 [quant-ph]

    work page doi:10.1038/s41598-019-46722-7 2019

  78. [78]

    Error mitigation for short-depth quantum circuits

    K. Temme, S. Bravyi, and J. M. Gambetta, Error Mitigation for Short-Depth Quantum Circuits, Phys. Rev. Lett.119, 180509 (2017), arXiv:1612.02058 [quant-ph]

    work page Pith review arXiv 2017

  79. [79]

    Li and S

    Y. Li and S. C. Benjamin, Efficient variational quantum simulator incorporating active error minimisation, arXiv e-prints , arXiv:1611.09301 (2016), arXiv:1611.09301 [quant-ph]

    work page arXiv 2016

  80. [80]

    Giurgica-Tiron, Y

    T. Giurgica-Tiron, Y. Hindy, R. LaRose, A. Mari, and W. J. Zeng, Digital zero noise extrapolation for quantum error miti- gation, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) , 306 (2020), arXiv:2005.10921 [quant-ph]

    work page arXiv 2020