Pith. sign in

REVIEW 4 major objections 6 minor 54 references

Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Computers

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read A hybrid quantum-classical algorithm computes ground-state energies of the XXZ spin chain to sub-percent accuracy by classically diagonalizing a symmetry-filtered subspace generated from a single short Trotter step.

desk verdict Plausible N=24 hardware results undermined by abstract overclaims and a missing error-bound derivation, but the core idea deserves a referee. read the letter →

arxiv 2512.12753 v2 pith:4QBVECTT submitted 2025-12-14 cond-mat.str-el quant-ph

Anutosh Biswas , Sayan Ghosh , Ritajit Majumdar , Mostafizur Rahaman Laskar , Nicholas Bronn , Manoranjan Kumar This is my paper
classification cond-mat.str-elquant-ph
keywords basisadaptivealgorithmhybridquantum-classicalsimulationground-stateenergyXXZspinchainsymmetryfilteringTrotterevolutionreducedHilbertspaceerrorbound
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces a Basis Adaptive algorithm that replaces variational optimization and deep phase-estimation circuits with a short, noisy real-time evolution step on a quantum processor. Starting from two Néel bitstrings, it applies one Trotter step, samples the evolved states, filters by total spin and reflection symmetry, and exactly diagonalizes the Hamiltonian in the resulting reduced Hilbert space. The authors establish an analytic error bound connecting the energy error to the probability weight captured by the sampled basis, and they demonstrate sub-percent ground-state errors for the spin-1/2 XXZ chain up to 24 qubits in the gapped antiferromagnetic regime. If correct, this provides a noise-resilient, near-term path to ground-state properties for correlated systems where the ground state is sparse in a physically motivated basis.

What carries the argument

The central mechanism is the one-step Trotterized time evolution used as a basis generator: it spreads a few initial computational-basis states into a subspace that contains the dominant ground-state components, while U(1) total-spin conservation and lattice reflection symmetry filter out noise-induced leakage into symmetry-forbidden sectors. The analytical error bound ties algorithm performance directly to the ground-state probability weight α_{D_T} captured by the sampled basis, explaining why accuracy improves in more Ising-like regimes and degrades in critical regimes.

What would settle it

Compute the overlap α between the symmetry-filtered sampled basis and the exact ground state for N=24 at Δ=0.5; the claimed error bound predicts the energy error should approximately equal sqrt(8)||H||(1−sqrt(α))^{1/2}, so a measured error that deviates strongly from this prediction would falsify the analytical argument.

Watch

Extended reading notes

Core claim

The central claim is that a compact, symmetry-respecting basis for the ground state can be generated by evolving just two classical Néel configurations under a single first-order Trotter step with Δt=0.25 on quantum hardware, then post-selecting measurements that preserve total Sz and lattice reflection symmetry. The reduced Hamiltonian is diagonalized classically, yielding ground-state energies within 0.87% at the isotropic point Δ=1.0 and 0.38% at Δ=1.4 with wavefunction fidelity above 0.96. The paper also proves a general error bound: the ground-state energy error is at most sqrt(8)||H||(1−sqrt(α_{D_T}))^{1/2}, where α_{D_T} is the probability weight of the sampled basis states in the exa

Load-bearing premise

The entire basis-generation scheme assumes that a single short-time Trotter evolution of two Néel bitstrings produces a sampled subspace that contains the dominant ground-state components; this is argued only perturbatively in the Ising limit and is not guaranteed for critical systems or larger sizes.

Editorial extensions

If this is right

  • Ground-state energies of local spin Hamiltonians can be approximated on near-term hardware without variational optimization or deep coherent circuits.
  • The analytical error bound provides a practical stopping criterion: measure the sampled basis weight α and predict the energy error before performing the classical diagonalization.
  • The method's accuracy is directly tied to ground-state sparsity, so it is expected to work best in gapped, weakly entangled phases and to struggle in gapless or strongly fluctuating regimes.
  • Symmetry filtering is the key to noise resilience; hard noise that breaks the conserved quantities can be discarded by the post-selection step.
  • The work validates symmetry-filtered real-time sampling as an alternative to sampling-based Krylov methods, achieving a substantially lower energy error for comparable reduced-space dimensions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The approach could be extended to other one-dimensional models where a dominant product state is known, such as the Haldane chain or the SSH model, provided the initial bitstring is chosen appropriately.
  • The single Trotter step with Δt=0.25 appears to be a sweet spot; testing multiple shorter steps or optimized time steps could improve the sampled basis weight α in critical regimes like Δ=0.5, where the abstract reports a 28.7% error.
  • The error bound suggests a general design principle: the algorithm's success reduces to finding an initial set of bitstrings and a short evolution that maximize the overlap with the true ground state, which could be formalized as a variational problem over initial configurations.
  • A natural next step would be to test the algorithm on frustrated or higher-dimensional systems where the symmetry group is richer and the ground state is less sparse, to see if the symmetry-filtering step remains sufficient.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper introduces a Basis Adaptive (BA) hybrid quantum-classical algorithm for computing ground-state properties of quantum many-body systems. Starting from two Néel bitstrings, the algorithm applies a single first-order Trotter step with Δt=0.25 on IBM Heron hardware, measures the evolved states, post-selects sampled bitstrings by total Sz conservation and lattice reflection symmetry, and classically diagonalizes the XXZ Hamiltonian in the resulting reduced subspace. The procedure is iterated by retaining the m1 most probable basis states from the diagonalization. For N=24, the paper reports sub-percent ground-state energy errors for Δ=1.0 (0.87%), 1.2 (0.64%), and 1.4 (0.38%), high fidelities (F>0.96), and accurate spin-spin correlation functions. A comparison with Sampling Krylov Quantum Diagonalization (SKQD) is also presented. The abstract additionally claims an analytical error bound of sqrt(8)||H||(1−sqrt(α_D_T))^{1/2} and benchmarks up to N=62 with specific errors at Δ=2.0, −1.0, and 0.5; these results are absent from the body of the paper and the supplemental material.

Significance. If the reported claims are substantiated, the algorithm would be a practically relevant hybrid quantum-classical method for ground-state simulations using only shallow Trotter circuits, avoiding VQE optimization landscapes and QPE circuit depth. The N=24 hardware results in Table I and the reproduced correlation functions are genuinely interesting and provide a proof-of-principle that symmetry-filtered, real-time sampling can be used to build a variational subspace. However, the paper's strongest advertised results—the analytical error bound and the N=62, Δ=2.0/−1.0/0.5 benchmarks—are not supported by any derivation or data in the manuscript. The SKQD comparison in Table II is not on equal footing because the BA subspace is approximately 12 times larger. These issues are load-bearing for the abstract's claims and for the stated superiority over SKQD. With a major revision that either adds the missing evidence or scales back the claims to what the body demonstrates, the work could be a useful contribution.

major comments (4)
  1. [Abstract vs. §IV–V and Table I] The abstract reports benchmarks on 'up to N=62 qubits' with energy errors of 3.5% (Δ=2.0), <0.5% (Δ=−1.0), and 28.7% (Δ=0.5). None of these results appear in the main text or the supplementary material. The body restricts itself to N=24 and to Δ=1.0, 1.2, 1.4 in Table I and Figs. 3–4. Since the abstract is the primary statement of the paper's contribution, this is a serious disconnect. Please either include the N=62 data and the Δ=2.0/−1.0/0.5 results with a full description of the runs, or revise the abstract and summary to match the N=24 evidence presented.
  2. [Abstract, Eq. (unnumbered); §III–IV] The claimed analytical error bound, sqrt(8)||H||(1−sqrt(α_{D_T}))^{1/2}, is never derived in the main text or the SM. The quantities α_{D_T} and D_T are not defined in the body; the bound is therefore disconnected from the data. Moreover, no measurement or estimate of α_{D_T} is reported for the subspaces in Table I. Since the abstract states that this bound 'explains the observed accuracy hierarchy,' it is essential to provide the derivation and to report α_{D_T} for at least the N=24 cases.
  3. [§IV D, Table II; §V summary] Table II compares SKQD with subspace dimension 39,733 against the BA algorithm with dimension 469,004—a factor of ≈11.8 difference. The text and summary describe these as 'comparable reduced-space dimensions' and use them to claim that the BA 'outperforms SKQD.' This is contradicted by the table itself. A fair comparison should use similar subspace sizes, or the authors should explicitly discuss how the accuracy scales with subspace dimension and justify the comparison. As written, the claim is not supported.
  4. [§III Step 2, §IV A, SM §S5] The central mechanism of the algorithm is that a single first-order Trotter step (Δt=0.25) from the two Néel states, sampled with 40,000 shots and then symmetry-filtered, produces a basis containing the dominant components of the true ground state. The only theoretical support offered is the perturbative Ising-limit analysis in SM §S5, which assumes γ=1/Δ is small and shows numerical checks at γ=0.1 and 0.05 (Δ=10 and 20), not at Δ=1.0 where the flagship 0.87% error is reported. The paper never reports α_{D_T}, i.e., the overlap of the final 469,004-state subspace with the exact ground state. Consequently, the observed accuracy could in principle be an artifact of the large subspace size (~17% of the full Sz=0 sector) rather than of the sampling strategy. Please report α_{D_T} or otherwise test the sampling hypothesis, for example by comparing with a randomly chosen subspace of the same
minor comments (6)
  1. [References] Several references have incomplete author lists, e.g., Refs. [39]–[43] list 'M. M. et al.' or 'S. M. et al.' These need to be completed.
  2. [Eq. (12)] The fidelity is defined as F = ⟨ψ_{gs}^{BA}|ψ_{gs}^{ED}⟩. Since the overlap can be complex, the absolute value should be used, and the normalization of the states should be stated explicitly.
  3. [Abstract vs. §V] The abstract states 'up to N=62 qubits on the IBM Heron processor,' while Section V states 'up to N=24 qubits (on IBM's Heron).' These are inconsistent and should be reconciled.
  4. [Table I caption] The caption says 'The total Hilbert space dimension is 2704156.' This is the dimension of the Sz=0 sector for N=24, not the full Hilbert space (which is 2^24). Please use precise terminology.
  5. [Fig. 3] In the text, Fig. 3(a) is said to show dependence on m1 for two Ms values and Fig. 3(b) for several Δ; the figure panels appear to be ordered differently. Please check the panel labels and the in-text references.
  6. [§IV A] The sentence 'this accuracy is achieved only by recovering around 18% of the total Hilbert space' is slightly inconsistent with Table I: 469,004/2,704,156 ≈ 17.3%. Also, ensure 'total Hilbert space' is replaced with 'Sz=0 sector' as above.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported energies are variational eigenvalues in a Trotter-sampled, symmetry-filtered subspace, not fitted predictions; the one overlapping-author citation is not load-bearing.

full rationale

The central derivation is not circular. Section III step 4 constructs the Hamiltonian in the sampled, symmetry-filtered subspace and classically diagonalizes it; the reported energies and fidelities in Table I are then compared against exact diagonalization from Section II, an external benchmark. The abstract's error bound is a genuine variational/Rayleigh-Ritz type bound: for any subspace with overlap α_{D_T}, the eigenvalue error is controlled by ‖H‖(1−√α_{D_T})^{1/2}; α_{D_T} is an empirical overlap of the sampled basis with the true ground state, not a parameter fitted to the benchmark energies. The only overlapping-author citation is [48], used for the iterative 'keep the most probable basis states' update; the present algorithm's quantum Trotter sampling, symmetry filtering, and subsequent exact-diagonalization benchmarks are self-contained, so this citation is not load-bearing. Concerns about the unverified value of α_{D_T}, the perturbative justification being restricted to the Ising limit (SM §S5), and the large subspace needed at Δ=1.0 are external-validity/correctness issues, not circular reductions. No fitted input is renamed a prediction, and no uniqueness claim imports the conclusion.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new physical entities are proposed. The free parameters are algorithmic hyperparameters, and the key domain assumption is that Néel-seeded short-time evolution generates the relevant ground-state basis, which is only perturbatively motivated and fails in the critical regime per the abstract.

free parameters (4)
  • Trotter time step Δt = 0.25
    Chosen for the single evolution step; controls which basis states are generated and the Trotter error.
  • Retained basis count m1 = 96 (principal results)
    Number of most probable bitstrings kept after first iteration; accuracy improves with m1.
  • Measurement shots Ms = 40,000
    Number of samples per evolved state; controls sampling noise in basis reconstruction.
  • Number of iterations = 2
    All reported results are after second iteration; convergence criterion not specified.
assumptions (4)
  • domain assumption The XXZ ground state is dominated by basis states reachable by short-time evolution from two Néel bitstrings.
    Required for Step 1 and Section IV; violated for Δ=0.5 according to abstract's 28.7% error, and only argued perturbatively in Ising limit in SM S5.
  • domain assumption First-order Trotter error O(Δt^2) is negligible at Δt=0.25 for the sampled basis.
    Used in Eq. (11) and circuit; no convergence study in Δt is presented.
  • domain assumption Sz conservation and reflection symmetry are sufficient filters to remove noise-induced leakage and recover the relevant subspace.
    Step 3 of Section III; no check that other symmetries or error mitigation are needed.
  • domain assumption Finite-shot sampling (40K) faithfully represents the evolved state's probability distribution.
    Section IV A; no statistical error propagation to energies.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Computers." pith.science (2026). https://pith.science/paper/4QBVECTT

@misc{pith2026251212753,
  author       = {Pith},
  title        = {Pith review of: Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Computers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4QBVECTT}},
  note         = {Machine review of arXiv:2512.12753}
}
abstract

We introduce a Basis Adaptive (BA) algorithm for hybrid quantum-classical simulation of correlated quantum many-body systems. Starting from a small set of physically motivated bitstrings, the algorithm iteratively applies a single-step first-order Trotterized circuit on a quantum processor, filters the sampled configurations by enforcing $U(1)$ spin conservation and lattice reflection symmetry, and classically diagonalizes the Hamiltonian in the resulting reduced Hilbert space. This design avoids the variational optimization overhead of VQE, the deep coherent circuits required by QPE, and the symmetry-violating subspaces that arise in SKQD. The ground-state energy error is bounded analytically by $\sqrt{8}\,\|H\|\left(1-\sqrt{\alpha_{D_T}}\right)^{1/2}$, where $\alpha_{D_T}$ is the probability weight captured by the $D_T$ sampled basis states. This bound connects algorithm performance directly to ground-state sparsity and explains the observed accuracy hierarchy across different phases. Benchmarked on the spin-$1/2$ Heisenberg XXZ chain (up to $N=62$ qubits on the IBM Heron processor), the algorithm achieves a $3.5\%$ energy error in the gapped Neel phase ($\Delta=2.0$) and below $0.5\%$ at the ferromagnetic boundary ($\Delta=-1.0$). The accuracy degrades to $28.7\%$ in the strongly quasi-long-range-ordered regime ($\Delta=0.5$). Spin-spin correlation functions are reproduced across all regimes, confirming that symmetry-filtered real-time sampling provides a practical and noise-resilient pathway to ground-state properties on near-term quantum hardware.

Figures

Figures reproduced from arXiv: 2512.12753 by the authors.

Figure 1
Figure 1. FIG. 1. Trotterized quantum circuit for the XXZ Hamil [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic workflow of the Basis Adaptive Algorithm. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. For different ∆ values correlation function is shown [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (1 more)
Figure 1
Figure 1. Figure 1: FIG. 1: Trotterized quantum circuit implementing one Trotter ste [PITH_FULL_IMAGE:figures/full_fig_p009_1.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

54 extracted references · 2 linked inside Pith

  1. [1]

    Each bitstring corre- sponds to a computational-basis state |b(0) k ⟩ within the Hilbert space of the system H

    Initialization: We prepare a small set of repre- sentative bitstrings, {b(0) k }, which encode the domi- nant spin configurations contributing to the ground state of the Hamiltonian H. Each bitstring corre- sponds to a computational-basis state |b(0) k ⟩ within the Hilbert space of the system H. Unlike con- ventional wavefunction-based approaches, we treat...

  2. [2]

    with J >0, the two rel- evant configurations are |b(0) 1 ⟩ = |↑↓↑↓ · · ·⟩, |b(0) 2 ⟩ = |↓↑↓↑ · · ·⟩

  3. [3]

    (9) For the XXZ Hamiltonian, H = ∑ j Hj, Hj = 1 2 ( S+ j S− j+1 +S− j S+ j+1 ) + ∆Sz jSz j+1

    Time Evolution: In the i-th iteration, each con- figuration |b(i) k ⟩ is evolved independently under the unitary operator U (∆t) = e−iH∆t: |b(i)′ k ⟩ =e−iH∆t |b(i) k ⟩. (9) For the XXZ Hamiltonian, H = ∑ j Hj, Hj = 1 2 ( S+ j S− j+1 +S− j S+ j+1 ) + ∆Sz jSz j+1. (10) Using the first-order Lie–Trotter decomposition, e−iH∆t ≈ ∏ j e−iHj ∆t + O((∆t)2), (11) eac...

  4. [4]

    The complete set of bitstrings generated from all evolved config- urations is then combined to form their union, B(i)′ = ⋃ k {b(i)′ k }

    Measurement, Union, and Symmetry Filter- ing: In the third step, each evolved configuration |b(i)′ k ⟩ is measured in the computational basis to ob- tain a sequence of bitstrings {b(i)′ k }. The complete set of bitstrings generated from all evolved config- urations is then combined to form their union, B(i)′ = ⋃ k {b(i)′ k }. From this unified set B(i)′ , we...

  5. [5]

    Within this reduced subspace, we construct the Hamilto- nian matrix corresponding to H and perform an exact diagonalization on a classical computer

    Hilbert-Space Reconstruction and Classical Diagonalization: In the fourth step, the filtered and symmetrized bitstrings {b(i)′ s } define the re- duced Hilbert space for the next iteration. Within this reduced subspace, we construct the Hamilto- nian matrix corresponding to H and perform an exact diagonalization on a classical computer. The lowest eigenvalu...

  6. [6]

    These most probable bases {bi m} work as initial basis set for the next iteration ( i + 1)th and repeat the step two-five till the energy is converged

    In the fifth step, if our ground state energy is con- verged then we calculate all the relevant quantity like correlation functions, spin density etc and exit or we construct updated wavefunction retaining mi number of basis states which have highest proba- bility C 2 i in the ground state wavefunction. These most probable bases {bi m} work as initial basi...

  7. [7]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 (2010)

    2010

  8. [8]

    Moessner and A

    R. Moessner and A. P. Ramirez, Geometrical frustration, Physics Today 59, 24 (2006)

    2006

Show all 54 references
  1. [9]

    J. S. Gardner, M. J. Gingras, and J. E. Greedan, Mag- netic pyrochlore oxides, Rev. Mod. Phys. 82, 53 (2010)

    2010

  2. [10]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a mott in- sulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006)

    2006

  3. [11]

    D. J. Scalapino, A common thread: The pairing inter- action for unconventional superconductors, Rev. Mod. Phys. 84, 1383 (2012)

    2012

  4. [12]

    Keimer, S

    B. Keimer, S. A. Kivelson, M. R. Norman, S.-i. Uchida, and J. Zaanen, From quantum matter to high- temperature superconductivity in copper oxides, Nature 518, 179 (2015)

    2015

  5. [13]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Rep. Prog. Phys. 80, 016502 (2017)

    2017

  6. [14]

    Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017)

    2017

  7. [15]

    S. Yan, D. A. Huse, and S. R. White, Spin-liquid ground state of the s=1/2 kagome heisenberg antiferromagnet, Science 332, 1173 (2011)

    2011

  8. [16]

    P. W. Anderson, The resonating valence bond state in La 2CuO4 and superconductivity, Science 235, 1196 (1987)

    1987

  9. [17]

    Imada, A

    M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998)

    1998

  10. [18]

    G. D. Mahan, Many Particle Physics, Third Edition (Plenum, New York, 2000)

    2000

  11. [19]

    A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Boston, 1971). 7

    1971

  12. [20]

    A. W. Sandvik, Computational studies of quantum spin systems, in AIP Conference Proceedings, Vol. 1297 (American Institute of Physics, 2010) pp. 135–338

    2010

  13. [21]

    Lin, Exact diagonalization of quantum-spin models, Physical Review B 42, 6561 (1990)

    H. Lin, Exact diagonalization of quantum-spin models, Physical Review B 42, 6561 (1990)

    1990

  14. [22]

    Nataf and F

    P. Nataf and F. Mila, Exact diagonalization of heisenbe rg su (n) models, Physical review letters 113, 127204 (2014)

    2014

  15. [23]

    W. M. Foulkes, L. Mitas, R. Needs, and G. Rajagopal, Quantum monte carlo simulations of solids, Reviews of Modern Physics 73, 33 (2001)

    2001

  16. [24]

    Pollet, Recent developments in quantum monte carlo simulations with applications for cold gases, Reports on progress in physics 75, 094501 (2012)

    L. Pollet, Recent developments in quantum monte carlo simulations with applications for cold gases, Reports on progress in physics 75, 094501 (2012)

    2012

  17. [25]

    Gubernatis, N

    J. Gubernatis, N. Kawashima, and P. Werner, Quan- tum Monte Carlo Methods (Cambridge University Press, 2016)

    2016

  18. [26]

    A. W. Sandvik and J. Kurkij¨ arvi, Quantum monte carlo simulation method for spin systems, Physical Review B 43, 5950 (1991)

    1991

  19. [27]

    Ceperley and B

    D. Ceperley and B. Alder, Quantum monte carlo, Science 231, 555 (1986)

    1986

  20. [28]

    R. R. d. Santos, Introduction to quantum monte carlo simulations for fermionic systems, Brazilian Journal of Physics 33, 36 (2003)

    2003

  21. [29]

    Montangero, E

    S. Montangero, E. Montangero, and Evenson, Introduc- tion to tensor network methods (Springer, 2018)

    2018

  22. [30]

    M. C. Ba˜ nuls, Tensor network algorithms: A route map, Annual Review of Condensed Matter Physics 14, 173 (2023)

    2023

  23. [31]

    S.-J. Ran, E. Tirrito, C. Peng, X. Chen, L. Tagliacozzo, G. Su, and M. Lewenstein, Tensor network contractions: methods and applications to quantum many-body systems (Springer Nature, 2020)

    2020

  24. [32]

    Fishman, S

    M. Fishman, S. White, and E. M. Stoudenmire, The iten- sor software library for tensor network calculations, Sci- Post Physics Codebases , 004 (2022)

    2022

  25. [33]

    Pan and Z

    G. Pan and Z. Y. Meng, Sign problem in quantum monte carlo simulation, arXiv preprint arXiv:2204.08777 (2022)

    2022 arXiv

  26. [34]

    Troyer and U.-J

    M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations, Physical review letters 94, 170201 (2005)

    2005

  27. [35]

    Schollw¨ ock, The density-matrix renormalization group, Rev

    U. Schollw¨ ock, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005)

    2005

  28. [36]

    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 Reports 986, 1 (2022)

    2022

  29. [37]

    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, nature 549, 242 (2017)

    2017

  30. [38]

    Liu, Y.-H

    J.-G. Liu, Y.-H. Zhang, Y. Wan, and L. Wang, Varia- tional quantum eigensolver with fewer qubits, Physical Review Research 1, 023025 (2019)

    2019

  31. [39]

    Zhang, L

    Y. Zhang, L. Cincio, C. F. Negre, P. Czarnik, P. J. Coles, P. M. Anisimov, S. M. Mniszewski, S. Tretiak, and P. A. Dub, Variational quantum eigensolver with reduced cir- cuit complexity, npj Quantum Information 8, 96 (2022)

    2022

  32. [40]

    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 communications 5, 4213 (2014)

    2014

  33. [41]

    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)

    2018

  34. [42]

    Kitaev, Quantum measurements and the abelian sta- bilizer problem, arXiv:quant-ph/9511026 (1995)

    A. Kitaev, Quantum measurements and the abelian sta- bilizer problem, arXiv:quant-ph/9511026 (1995)

    1995 arXiv

  35. [43]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)

    2000

  36. [44]

    Yoshioka, M

    N. Yoshioka, M. Amico, W. Kirby, P. Jurcevic, A. Dutt, B. Fuller, S. Garion, H. Haas, I. Hamamura, A. Ivrii, et al. , Krylov diagonalization of large many-body hamil- tonians on a quantum processor, Nature Communica- tions 16, 5014 (2025)

    2025

  37. [45]

    M. M. et al., Hamiltonian simulation with krylov-space methods, PRX Quantum 2, 040314 (2021)

    2021

  38. [46]

    M. M. et al., Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution, Nat. Phys. 16, 205 (2020)

    2020

  39. [47]

    S. M. et al., Variational ansatz-based quantum simula- tion of imaginary time evolution, npj Quantum Inf. 5, 75 (2019)

    2019

  40. [48]

    A. M. C. et al., Toward the first quantum simulation with quantum speedup, PNAS 115, 9456 (2018)

    2018

  41. [49]

    Campbell, Random compiler for fast hamiltonian sim- ulation, Phys

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

    2019

  42. [50]

    Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

    T. Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

    2003

  43. [51]

    Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 1999)

    M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 1999)

    1999

  44. [52]

    A. W. Sandvik, Computational studies of quantum spin systems, AIP Conference Proceedings 1297, 135 (2010) , https://pubs.aip.org/aip/acp/article- pdf/1297/1/135/11407753/135 1 online.pdf

    2010

  45. [53]

    See Supplemental Material for providing the detailing of the trotterized quantum circuits and perturbation anal- ysis in relation to the main text

  46. [54]

    S. S. Rahaman, S. Haldar, and M. Kumar, Machine learn- ing approach to study quantum phase transitions of a frustrated one dimensional spin-1/2 system, Journal of Physics: Condensed Matter 35, 115603 (2023). Basis Adaptive Algorithm for Quantum Many-Body Systems on Quantum Com...

    2023

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.