pith. machine review for the scientific record. sign in

arxiv: 2603.25582 · v2 · submitted 2026-03-26 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

A unified quantum computing quantum Monte Carlo framework through structured state preparation

Giuseppe Buonaiuto , Antonio Marquez Romero , Brian Coyle , Annie E. Paine , Vicente P. Soloviev , Stefano Scali , Michal Krompiec
Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:31 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Monte Carlostate preparationvariational quantum eigensolverexcited statescombinatorial optimizationfinite temperaturequantum circuits
0
0 comments X

The pith

Task-adapted unitaries extend QCQMC to excited states, optimization and finite temperature while the diffusion step improves energy accuracy across domains.

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

The paper replaces standard VQE state preparation in QCQMC with specialized circuits matched to each task. Variational fast forwarding and VUMPO handle excited-state spectra, symmetry-preserving VQE addresses combinatorial optimization, and Haar-random unitaries enable finite-temperature estimates from pure-state dynamics. Benchmarks on molecular, condensed-matter, nuclear-structure and graph problems show the quantum Monte Carlo diffusion step consistently refines the energies obtained from these preparations. The unification matters because it lets one core diffusion process serve many variational quantum methods without redesigning the entire algorithm for each new problem class.

Core claim

Replacing the original VQE prescription with task-adapted unitaries (VFF, VUMPO, symmetry-preserving VQE, Haar-random) lets QCQMC address excited-state spectra, combinatorial optimization and finite-temperature observables. Benchmarks across molecular, condensed-matter, nuclear-structure and graph-optimization problems show the QMC diffusion step improves energy accuracy over the underlying state-preparation method in every domain. For weakly correlated systems VUMPO reaches near-exact energies with shallower circuits after classical tensor-network pre-training; for strongly correlated systems the diffusion correction becomes essential.

What carries the argument

Task-adapted state-preparation unitaries integrated with the QCQMC diffusion step, where the diffusion refines the prepared quantum states to lower variational energies.

If this is right

  • For weakly correlated systems, VUMPO plus classical pre-training yields near-exact energies with significantly shallower quantum circuits.
  • For strongly correlated systems the diffusion correction is required to reach useful accuracy.
  • Finite-temperature observables become accessible from pure-state dynamics via Haar-random basis preparation inside QCQMC.
  • The same diffusion layer improves results uniformly across molecular, condensed-matter, nuclear and graph problems.

Where Pith is reading between the lines

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

  • The framework could function as a general post-processing layer for other variational quantum algorithms once suitable unitaries are identified.
  • Classical tensor-network pre-training paired with shallow quantum circuits may improve scalability for larger systems where full variational optimization is expensive.
  • Choosing different structured unitaries might allow the same QCQMC core to tackle time-dependent or open-system problems.

Load-bearing premise

The task-adapted unitaries can be systematically built and combined with the diffusion step without introducing errors that cancel the accuracy gains.

What would settle it

An example in which the QCQMC diffusion step applied to a well-constructed task-adapted unitary produces a higher energy than the unitary alone, or a problem class for which no suitable task-adapted unitary can be constructed.

Figures

Figures reproduced from arXiv: 2603.25582 by Annie E. Paine, Antonio Marquez Romero, Brian Coyle, Giuseppe Buonaiuto, Michal Krompiec, Stefano Scali, Vicente P. Soloviev.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic workflow of the Cross-domain QCQMC. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Modified Hadamard test to compute the abso [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Modified Hadamard test to compute the transition [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Overview of the VUMPO ansatz. (a) An [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. pPhase diagram of the 2 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Configurational valence space for the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Ethylene molecule, composed of two carbon atoms [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. QCQMC results for the final energy, utilizing a VQE [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. QCQMC results for the final energy, utilizing a [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Trajectories of QCQMC with a VQE-prepared state [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. QCQMC results for the final energy, utilizing a [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Trajectories of QCQMC with a VFF-prepared state [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Ground-state trajectory results as a function of the [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Trajectories of QCQMC with a VUMPO-prepared [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Bitstring basis expansion results for two phases of [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Finite-temperature energy trajectory with QCQMC [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Finite-temperature energy trajectory with QCQMC [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Graph visualization and a valid partition for [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Trajectories of QCQMC with a VQE-prepared state [PITH_FULL_IMAGE:figures/full_fig_p018_19.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Bitstring basis expansion results for the QCQMC [PITH_FULL_IMAGE:figures/full_fig_p018_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Trajectories of QCQMC with a VUMPO-prepared [PITH_FULL_IMAGE:figures/full_fig_p019_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Bitstring basis expansion for the ground- and low [PITH_FULL_IMAGE:figures/full_fig_p019_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: FIG. 25. Energy convergence of the ground-state for the nu [PITH_FULL_IMAGE:figures/full_fig_p020_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26. Modified Hadamard test to compute the absolute [PITH_FULL_IMAGE:figures/full_fig_p026_26.png] view at source ↗
read the original abstract

We extend Quantum Computing Quantum Monte Carlo (QCQMC) beyond ground-state energy estimation by systematically constructing the quantum circuits used for state preparation. Replacing the original Variational Quantum Eigensolver (VQE) prescription with task-adapted unitaries, we show that QCQMC can address excited-state spectra via Variational Fast Forwarding and the Variational Unitary Matrix Product Operator (VUMPO), combinatorial optimization via a symmetry-preserving VQE ansatz, and finite-temperature observables via Haar-random unitaries. Benchmarks on molecular, condensed-matter, nuclear-structure, and graph-optimization problems demostrate that the QMC diffusion step consistently improves the energy accuracy of the underlying state-preparation method across all tested domains. For weakly correlated systems, VUMPO achieves near-exact energies with significantly shallower circuits by offloading optimization to a classical tensor-network pre-training step, while for strongly correlated systems, the QMC correction becomes essential. We further provide a proof-of-concept demonstration that Haar-random basis state preparation within QCQMC yields finite-temperature estimates from pure-state dynamics.

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

1 major / 1 minor

Summary. The paper extends QCQMC beyond ground-state estimation by replacing standard VQE state preparation with task-adapted unitaries (VFF for excited states, VUMPO for weakly correlated systems via classical tensor-network pre-training, symmetry-preserving VQE for combinatorial optimization, and Haar-random unitaries for finite-temperature observables). Benchmarks on molecular, condensed-matter, nuclear-structure, and graph-optimization problems are reported to show that the QMC diffusion step consistently improves energy accuracy over the underlying state-preparation methods, with VUMPO achieving near-exact results for weakly correlated cases and the diffusion correction becoming essential for strongly correlated regimes; a proof-of-concept for finite-temperature estimates from pure-state dynamics is also included.

Significance. If the reported benchmarks hold with adequate controls, the work offers a systematic unification of QCQMC with multiple quantum algorithms, enabling broader applicability while leveraging classical pre-training to reduce circuit depth in selected regimes. The consistent cross-domain improvement and the finite-temperature demonstration represent a meaningful advance in hybrid quantum-classical simulation frameworks.

major comments (1)
  1. The central claim of consistent accuracy improvement across domains rests on the benchmark comparisons, yet the manuscript must supply explicit numerical energy values, error bars, circuit depths, and statistical tests for each domain and method (including direct before/after diffusion comparisons) to allow independent evaluation; without these the improvement cannot be quantified or verified.
minor comments (1)
  1. Abstract: 'demostrate' is a typographical error and should read 'demonstrate'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation of minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: The central claim of consistent accuracy improvement across domains rests on the benchmark comparisons, yet the manuscript must supply explicit numerical energy values, error bars, circuit depths, and statistical tests for each domain and method (including direct before/after diffusion comparisons) to allow independent evaluation; without these the improvement cannot be quantified or verified.

    Authors: We agree that explicit numerical values are required for independent verification. In the revised manuscript we add Table II, which tabulates, for every domain and method: the raw energy (or observable) from the state-preparation unitary alone, the energy after the QCQMC diffusion step, the Monte Carlo statistical error bars, the circuit depth of the preparation unitary, and the p-value from a paired t-test on the before/after improvement. Direct before/after columns are included for all four domains (molecular, condensed-matter, nuclear, graph). revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper extends QCQMC by replacing VQE with task-adapted unitaries (VFF, VUMPO, symmetry-preserving VQE, Haar-random) for different regimes and demonstrates via benchmarks that the diffusion step improves energy accuracy across molecular, condensed-matter, nuclear, and graph problems. No equations, definitions, or self-citations in the abstract or described chain reduce the claimed improvements to fitted parameters, self-referential quantities, or load-bearing prior results by the same authors. The constructions and benefits are presented as independent extensions validated externally rather than derived tautologically from the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The framework implicitly assumes efficient classical pre-training for VUMPO and unbiased diffusion in QCQMC, but these cannot be audited from the given text.

pith-pipeline@v0.9.0 · 5506 in / 1065 out tokens · 39663 ms · 2026-05-15T00:31:22.009188+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

118 extracted references · 118 canonical work pages · 1 internal anchor

  1. [1]

    Despite its simplicity, it shows a wide variety of phenomena, even in its one-dimensional formulation [83]

    2D Fermi-Hubbard model One of the cornerstone models of electronic systems and materials is the Fermi-Hubbard model. Despite its simplicity, it shows a wide variety of phenomena, even in its one-dimensional formulation [83]. In two dimensions, the Fermi-Hubbard Hamiltonian is considered a non- trivial benchmark for studying strongly correlated sys- tems a...

    work page

  2. [2]

    This involves treating protons and neutrons (nucleons) as fundamental fermions that occupy single- particle states, or orbitals, within a valence space as shown in Fig

    Nuclear shell model In the nuclear shell model, atomic nuclei are described similarly to how molecules are described in quantum chemistry. This involves treating protons and neutrons (nucleons) as fundamental fermions that occupy single- particle states, or orbitals, within a valence space as shown in Fig. 6. These orbitals are characterized by quantum nu...

    work page

  3. [3]

    misordering

    Cardinality-Constrained MaxCut Optimization Optimization problems defined on graphs play a cen- tral role in combinatorial optimization, where the ob- jective is to make decisions based on the structure and weights of vertices and edges. The cost function in Eq. (24) defines acardinality-constrained MaxCut prob- lemon a graphG= (V, E), whereVis the set of...

    work page

  4. [4]

    M. B. Donnelly, Y. Chung, R. Garreis, S. Plugge, D. Pye, M. Kiczynski, J. T´ amara-Isaza, M. M. Mu- nia, S. Sutherland, B. Voisin, L. Kranz, Y. L. Hsueh, A. M. S.-E. Huq, C. R. Myers, R. Rahman, J. G. Keizer, S. K. Gorman, and M. Y. Simmons, Large-scale ana- logue quantum simulation using atom dot arrays, Na- ture650, 574 (2026)

    work page 2026

  5. [5]

    W.-W. Fan, L. J. Hong, G.-X. Jiang, and J. Luo, Review of large-scale simulation optimization, Journal of the Operations Research Society of China13, 688 (2025)

    work page 2025

  6. [6]

    S. E. Venegas-Andraca, Quantum walks: a comprehen- sive review, Quantum Information Processing11, 1015 (2012)

    work page 2012

  7. [7]

    F. R. Petruzielo, A. A. Holmes, H. J. Changlani, M. P. Nightingale, and C. J. Umrigar, Semistochastic projec- tor monte carlo method, Phys. Rev. Lett.109, 230201 (2012)

    work page 2012

  8. [8]

    X. Hu, Y. Nonomura, and M. Kohno, Monte carlo simu- lation, inSpringer Handbook of Materials Measurement Methods, edited by H. Czichos, T. Saito, and L. Smith (Springer Berlin Heidelberg, Berlin, Heidelberg, 2006) pp. 1057–1096

    work page 2006

  9. [9]

    B. M. Austin, D. Y. Zubarev, and W. A. Lester Jr., Quantum monte carlo and related approaches, Chemical Reviews112, 263 (2012)

    work page 2012

  10. [10]

    Pan and Z

    G. Pan and Z. Y. Meng, The sign problem in quan- tum monte carlo simulations, inEncyclopedia of Con- densed Matter Physics (Second Edition), edited by T. Chakraborty (Academic Press, Oxford, 2024) second edition ed., pp. 879–893

    work page 2024

  11. [11]

    Carlson, S

    J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schiavilla, K. E. Schmidt, and R. B. Wiringa, Quan- tum monte carlo methods for nuclear physics, Reviews of modern physics87, 1067 (2015)

    work page 2015

  12. [12]

    G. H. Booth, A. J. Thom, and A. Alavi, Fermion monte carlo without fixed nodes: A game of life, death, and annihilation in slater determinant space, The Journal of Chemical Physics131, 054106 (2009)

    work page 2009

  13. [13]

    Cleland, G

    D. Cleland, G. H. Booth, C. Overy, and A. Alavi, Tam- ing the first-row diatomics: A full configuration inter- action quantum monte carlo study, Journal of chemical theory and computation8, 4138 (2012)

    work page 2012

  14. [14]

    M. H. Kolodrubetz, J. S. Spencer, B. K. Clark, and W. M. Foulkes, The effect of quantization on the full configuration interaction quantum monte carlo sign problem, The Journal of Chemical Physics138, 024110 (2013)

    work page 2013

  15. [15]

    Troyer and U.-J

    M. Troyer and U.-J. Wiese, Computational complex- ity and fundamental limitations to fermionic quantum monte carlo simulations, Phys. Rev. Lett.94, 170201 (2005)

    work page 2005

  16. [16]

    G. H. Booth and A. Alavi, Approaching chemical accu- racy using full configuration-interaction quantum monte carlo: A study of ionization potentials, The Journal of Chemical Physics132, 174104 (2010)

    work page 2010

  17. [17]

    Ghanem, K

    K. Ghanem, K. Guther, and A. Alavi, The adaptive shift method in full configuration interaction quantum monte carlo: Development and applications, The Journal of Chemical Physics153, 224115 (2020)

    work page 2020

  18. [18]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pear- son, M. Troyer, and P. Zoller, Practical quantum advan- tage in quantum simulation, Nature607, 667 (2022)

    work page 2022

  19. [19]

    H. Qi, S. Xiao, Z. Liu, C. Gong, and A. Gani, Varia- tional quantum algorithms: fundamental concepts, ap- plications and challenges, Quantum Information Pro- cessing23, 224 (2024)

    work page 2024

  20. [20]

    Mind the gaps: The fraught road to quantum advantage

    J. Eisert and J. Preskill, Mind the gaps: The fraught road to quantum advantage, arXiv preprint arXiv:2510.19928 (2025)

    work page arXiv 2025

  21. [21]

    Larocca, S

    M. Larocca, S. Thanasilp, S. Wang, K. Sharma, J. Bia- monte, P. J. Coles, L. Cincio, J. R. McClean, Z. Holmes, and M. Cerezo, Barren plateaus in variational quantum computing, Nature Reviews Physics7, 174 (2025)

    work page 2025

  22. [22]

    W. Saib, P. Wallden, and I. Akhalwaya, The effect of noise on the performance of variational algorithms for quantum chemistry, in2021 IEEE International Confer- ence on Quantum Computing and Engineering (QCE) (2021) pp. 42–53

    work page 2021

  23. [23]

    Kanno, H

    S. Kanno, H. Nakamura, T. Kobayashi, M. Bamba, and N. Yamamoto, Quantum computing quantum monte carlo with hybrid tensor network for electronic structure calculations, npj Quantum Information10, 48 (2024)

    work page 2024

  24. [24]

    Zhang, Y

    Y. Zhang, Y. Huang, J. Sun, D. Lv, and X. Yuan, Quan- tum computing quantum monte carlo algorithm, Phys. 22 Rev. A112, 022428 (2025)

    work page 2025

  25. [25]

    W. J. Huggins, B. A. O’Gorman, N. C. Rubin, D. R. Reichman, R. Babbush, and J. Lee, Unbiasing fermionic quantum monte carlo with a quantum computer, Nature 603, 416 (2022)

    work page 2022

  26. [26]

    A. W. Sandvik and G. Vidal, Variational quantum monte carlo simulations with tensor-network states, Phys. Rev. Lett.99, 220602 (2007)

    work page 2007

  27. [27]

    J. Chen, J. Jiang, D. Hangleiter, and N. Schuch, Sign problem in tensor-network contraction, PRX Quantum 6, 010312 (2025)

    work page 2025

  28. [28]

    Jiang, B

    T. Jiang, B. O’Gorman, A. Mahajan, and J. Lee, Un- biasing fermionic auxiliary-field quantum monte carlo with matrix product state trial wavefunctions, Phys. Rev. Res.7, 013038 (2025)

    work page 2025

  29. [29]

    Shepard, A

    S. Shepard, A. Scemama, S. Moroni, and C. Filippi, Op- timizing excited states in quantum monte carlo: A re- assessment of double excitations, The Journal of Chem- ical Physics163, 024119 (2025)

    work page 2025

  30. [30]

    Higgott, D

    O. Higgott, D. Wang, and S. Brierley, Variational Quan- tum Computation of Excited States, Quantum3, 156 (2019)

    work page 2019

  31. [31]

    De Grandi, A

    C. De Grandi, A. Polkovnikov, and A. W. Sandvik, Uni- versal nonequilibrium quantum dynamics in imaginary time, Phys. Rev. B84, 224303 (2011)

    work page 2011

  32. [32]

    Kolotouros, D

    I. Kolotouros, D. Joseph, and A. K. Narayanan, Accel- erating quantum imaginary-time evolution with random measurements, Phys. Rev. A111, 012424 (2025)

    work page 2025

  33. [33]

    N. S. Blunt, S. D. Smart, G. H. Booth, and A. Alavi, An excited-state approach within full configuration inter- action quantum monte carlo, The Journal of Chemical Physics143, 134117 (2015)

    work page 2015

  34. [34]

    N. S. Blunt, T. W. Rogers, J. S. Spencer, and W. M. C. Foulkes, Density-matrix quantum monte carlo method, Phys. Rev. B89, 245124 (2014)

    work page 2014

  35. [35]

    Egginger, K

    S. Egginger, K. Kirova, S. Bruckner, S. Hillmich, and R. Kueng, A rigorous quantum framework for inequality-constrained and multi-objective binary opti- mization: Quadratic cost functions and empirical eval- uations, arXiv preprint arXiv:2510.13987 (2025)

    work page arXiv 2025

  36. [36]

    Jordan and E

    P. Jordan and E. Wigner, ¨ uber das paulische ¨ aquivalenzverbot, Zeitschrift f¨ r Physik47, 631–651 (1928)

    work page 1928

  37. [37]

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

    work page 2002

  38. [38]

    Derby, J

    C. Derby, J. Klassen, J. Bausch, and T. Cubitt, Com- pact fermion to qubit mappings, Physical Review B 104, 035118 (2021)

    work page 2021

  39. [39]

    A. M. Childs and N. Wiebe, Hamiltonian simulation us- ing linear combinations of unitary operations, Quantum Information & Computation12, 901 (2012)

    work page 2012

  40. [40]

    Campbell, Random compiler for fast hamiltonian simulation, Phys

    E. Campbell, Random compiler for fast hamiltonian simulation, Phys. Rev. Lett.123, 070503 (2019)

    work page 2019

  41. [41]

    K. Wan, M. Berta, and E. T. Campbell, Random- ized quantum algorithm for statistical phase estimation, Phys. Rev. Lett.129, 030503 (2022)

    work page 2022

  42. [42]

    Ouyang, D

    Y. Ouyang, D. R. White, and E. T. Campbell, Compila- tion by stochastic hamiltonian sparsification, Quantum 4, 235 (2020)

    work page 2020

  43. [43]

    G¨ unther, F

    J. G¨ unther, F. Witteveen, A. Schmidhuber, M. Miller, M. Christandl, and A. Harrow, Phase estimation with partially randomized time evolution, arXiv preprint arXiv:2503.05647 (2025)

    work page arXiv 2025

  44. [44]

    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)

    work page 2025

  45. [45]

    Brand, M

    J. Brand, M. Yang, and E. Pahl, Stochastic differen- tial equation approach to understanding the population control bias in full configuration interaction quantum monte carlo, Phys. Rev. B105, 235144 (2022)

    work page 2022

  46. [46]

    Ghanem, N

    K. Ghanem, N. Liebermann, and A. Alavi, Population control bias and importance sampling in full configu- ration interaction quantum monte carlo, Phys. Rev. B 103, 155135 (2021)

    work page 2021

  47. [47]

    Anand, P

    A. Anand, P. Schleich, S. Alperin-Lea, P. W. Jensen, S. Sim, M. D´ ıaz-Tinoco, J. S. Kottmann, M. Degroote, A. F. Izmaylov, and A. Aspuru-Guzik, A quantum com- puting view on unitary coupled cluster theory, Chemical Society Reviews51, 1659 (2022)

    work page 2022

  48. [48]

    P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, S. Filipp, and I. Tavernelli, Quantum algorithms for electronic structure calcula- tions: Particle-hole hamiltonian and optimized wave- function expansions, Phys. Rev. A98, 022322 (2018)

    work page 2018

  49. [49]

    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)

    work page 2021

  50. [50]

    Cowtan, W

    A. Cowtan, W. Simmons, and R. Duncan, A generic compilation strategy for the unitary coupled cluster ansatz, arXiv preprint arXiv:2007.10515 (2020)

    work page arXiv 2007

  51. [51]

    B. T. Gard, L. Zhu, G. S. Barron, N. J. Mayhall, S. E. Economou, and E. Barnes, Efficient symmetry- preserving state preparation circuits for the variational quantum eigensolver algorithm, npj Quantum Informa- tion6, 10 (2020)

    work page 2020

  52. [52]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets, nature549, 242 (2017)

    work page 2017

  53. [53]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Bab- bush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications 9, 4812 (2018)

    work page 2018

  54. [54]

    E. R. Anschuetz and B. T. Kiani, Beyond barren plateaus: Quantum variational algorithms are swamped with traps, Nature Communications13, 7760 (2022)

    work page 2022

  55. [55]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth,et al., The variational quantum eigensolver: a review of meth- ods and best practices, Physics Reports986, 1 (2022)

    work page 2022

  56. [56]

    Peruzzo, J

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.- Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, A variational eigenvalue solver on a photonic quantum processor, Nature Communications5, 4213 (2014)

    work page 2014

  57. [57]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru- Guzik, The theory of variational hybrid quantum- classical algorithms, New Journal of Physics18, 023023 (2016)

    work page 2016

  58. [58]

    Cirstoiu, Z

    C. Cirstoiu, Z. Holmes, J. Iosue, L. Cincio, P. J. Coles, and A. Sornborger, Variational fast forwarding for quan- tum simulation beyond the coherence time, npj Quan- tum Information6, 82 (2020)

    work page 2020

  59. [59]

    Abbas, R

    A. Abbas, R. King, H.-Y. Huang, W. J. Huggins, R. Movassagh, D. Gilboa, and J. McClean, On quan- tum backpropagation, information reuse, and cheating 23 measurement collapse, Advances in Neural Information Processing Systems36, 44792 (2023)

    work page 2023

  60. [60]

    Bowles, D

    J. Bowles, D. Wierichs, and C.-Y. Park, Backpropaga- tion scaling in parameterised quantum circuits, Quan- tum9, 1873 (2025)

    work page 2025

  61. [61]

    Dborin, F

    J. Dborin, F. Barratt, V. Wimalaweera, L. Wright, and A. G. Green, Matrix product state pre-training for quantum machine learning, Quantum Science and Tech- nology7, 035014 (2022)

    work page 2022

  62. [62]

    Dborin, V

    J. Dborin, V. Wimalaweera, F. Barratt, E. Ostby, T. E. O’Brien, and A. G. Green, Simulating groundstate and dynamical quantum phase transitions on a supercon- ducting quantum computer, Nature Communications 13, 5977 (2022)

    work page 2022

  63. [63]

    Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer

    L. Gover, V. Wimalaweera, F. Azad, M. DeCross, M. Foss-Feig, and A. G. Green, Fully optimised vari- ational simulation of a dynamical quantum phase tran- sition on a trapped-ion quantum computer, arXiv preprint arXiv:2502.06961 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  64. [64]

    Gibbs, L

    J. Gibbs, L. Cincio, C. Sarma, Z. Holmes, and P. Steven- son, Lowt-count preparation of nuclear eigenstates with tensor networks, arXiv preprint arXiv:2603.11156 (2026)

    work page arXiv 2026

  65. [65]

    Recio-Armengol, S

    E. Recio-Armengol, S. Ahmed, and J. Bowles, Train on classical, deploy on quantum: scaling generative quantum machine learning to a thousand qubits, arXiv preprint arXiv:2503.02934 (2025)

    work page arXiv 2025

  66. [66]

    Herrero-Gonzalez, B

    M. Herrero-Gonzalez, B. Coyle, K. McDowall, R. Grassie, S. Beentjes, A. Khamseh, and E. Kashefi, The born ultimatum: Conditions for classical surro- gation of quantum generative models with correlators, arXiv preprint arXiv:2511.01845 (2025)

    work page arXiv 2025

  67. [67]

    M. S. Rudolph, J. Miller, D. Motlagh, J. Chen, A. Acharya, and A. Perdomo-Ortiz, Synergistic pre- training of parametrized quantum circuits via tensor networks, Nature Communications14, 8367 (2023)

    work page 2023

  68. [68]

    M. C. Ba˜ nuls, Tensor Network Algorithms: A Route Map, Annual Review of Condensed Matter Physics14, 173 (2023)

    work page 2023

  69. [69]

    Or´ us, Tensor networks for complex quantum systems, Nature Reviews Physics1, 538 (2019), springer Nature

    R. Or´ us, Tensor networks for complex quantum systems, Nature Reviews Physics1, 538 (2019), springer Nature

    work page 2019

  70. [70]

    M. D. Garc´ ıa and A. M´ arquez Romero, Survey on com- putational applications of tensor-network simulations, IEEE Access12, 193212 (2024)

    work page 2024

  71. [71]

    Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of Physics349, 117 (2014)

    R. Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of Physics349, 117 (2014)

    work page 2014

  72. [72]

    Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of physics326, 96 (2011)

    U. Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of physics326, 96 (2011)

    work page 2011

  73. [73]

    S. R. White, Density matrix formulation for quantum renormalization groups, Physical review letters69, 2863 (1992)

    work page 1992

  74. [74]

    G. K.-L. Chan, J. J. Dorando, D. Ghosh, J. Hachmann, E. Neuscamman, H. Wang, and T. Yanai, An introduc- tion to the density matrix renormalization group ansatz in quantum chemistry, inFrontiers in quantum systems in chemistry and physics(Springer, 2008) pp. 49–65

    work page 2008

  75. [75]

    E. M. Stoudenmire and S. R. White, Studying two- dimensional systems with the density matrix renormal- ization group, Annu. Rev. Condens. Matter Phys.3, 111 (2012)

    work page 2012

  76. [76]

    Ganahl, J

    M. Ganahl, J. Beall, M. Hauru, A. G. Lewis, T. Wo- jno, J. H. Yoo, Y. Zou, and G. Vidal, Density ma- trix renormalization group with tensor processing units, PRX quantum4, 010317 (2023)

    work page 2023

  77. [77]

    Pollmann, V

    F. Pollmann, V. Khemani, J. I. Cirac, and S. L. Sondhi, Efficient variational diagonalization of fully many-body localized hamiltonians, Physical Review B94, 041116 (2016)

    work page 2016

  78. [78]

    Yoshioka, H

    N. Yoshioka, H. Hakoshima, Y. Matsuzaki, Y. Toku- naga, Y. Suzuki, and S. Endo, Generalized quantum subspace expansion, Phys. Rev. Lett.129, 020502 (2022)

    work page 2022

  79. [79]

    Scali, C

    S. Scali, C. Umeano, and O. Kyriienko, The topology of data hides in quantum thermal states, APL Quantum 1, 10.1063/5.0209201 (2024)

    work page doi:10.1063/5.0209201 2024

  80. [80]

    P lodzie´ n, Lecture notes on information scrambling, quantum chaos, and haar-random states, arXiv preprint arXiv:2511.14397 (2025)

    M. P lodzie´ n, Lecture notes on information scrambling, quantum chaos, and haar-random states, arXiv preprint arXiv:2511.14397 (2025)

    work page arXiv 2025

Showing first 80 references.