Pith. sign in

REVIEW 4 major objections 4 minor 230 references

The paper claims a concrete quantum-classical crossover for fault-tolerant simulation of mixed-field Ising dynamics: at physical error rates of 10^-3 and 10^-4, quantum machines with a few hundred thousand surface-code qubits should outperf

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

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

T0 review · deepseek-v4-flash

2026-08-01 21:17 UTC pith:OJNSD2WB

load-bearing objection Serious full-stack effort, but the headline crossover numbers don't survive contact with the paper's own Trotter fits and classical runtime claims. the 4 major comments →

arxiv 2607.16116 v1 pith:OJNSD2WB submitted 2026-07-17 quant-ph cond-mat.str-elhep-thmath-phmath.MP

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

Jinzhao Sun , Bozhen Zhou , Jue Xu , Yuan Yao , Zhenyu Du , Zixu Zhang , Yuntian Gu , Junxiang Huang
show 23 more authors
Shuo Zhou Ziruo Wang Alexander Yosifov Wenzheng Dong Yiming Huang Daniel Serrano Xinzhao Wang Tianfeng Feng Shreyas Sadugol Wenjun Yu Zhou You Dayue Qin Xiao-Ming Zhang Yantao Wu Aditya Iyer You Zhou Tongyang Li Ying Li Xiongfeng Ma Qi Zhao Pei Zeng Pan Zhang Xiao Yuan
This is my paper
classification quant-ph cond-mat.str-elhep-thmath-phmath.MP
keywords fault-tolerant quantum computationquantum-classical crossoverHamiltonian simulationmixed-field Ising modelTrotter errortensor networksobservable estimationrotation-state injection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to pin down when a fault-tolerant quantum computer would actually outrun the best classical algorithms for a specific practical task: simulating the real-time dynamics of the mixed-field Ising model. It claims the crossover happens at modest sizes—around 18–22 sites in 1D and around 26 sites against exact state-vector methods in 2D—under realistic hardware assumptions. The headline numbers are that a 100-site 1D simulation to time t = n/2 would take about 2 hours using 3.7 × 10^5 physical qubits at physical error rate 10^-3, while tensor-network classical simulations would take roughly a century or more. The route to this crossover is a full-stack co-design: entanglement-aware Trotter error bounds, a Gaussian-sampled Chebyshev amplitude estimation routine that balances circuit depth against sampling cost, and direct surface-code-protected injection of small-angle rotations whose residual logical error scales quadratically with the physical error rate.

Core claim

On the paper's own terms, the central discovery is a quantitative, resource-counted crossover where fault-tolerant quantum simulation beats the best classical baselines for a non-integrable many-body model. For the 1D mixed-field Ising model at target precision 0.01, the required MPS bond dimension grows exponentially with system size and the classical runtime as roughly e^{0.44n}, while the co-designed fault-tolerant estimate grows only polynomially; the crossover appears at n ≈ 18–22, and at n = 100 the quantum estimate is about 2 hours at p = 10^-3 and about 3 minutes at p = 10^-4. In 2D, tensor-network methods cannot push the simulation error below about 0.05 for n ≥ 20 at the light-cone

What carries the argument

The argument rests on three linked components. First, Gaussian-sampled Chebyshev amplitude estimation (GCAE): an observable-estimation circuit that samples the number of coherent queries to the time-evolution operator from a truncated Gaussian distribution, fits the result using Chebyshev polynomials, and interpolates between Heisenberg-limited depth and standard shot-noise sampling, thereby setting the balance between circuit depth and sampling overhead. Second, entanglement-informed Trotter step counting: instead of worst-case operator-norm commutator bounds, the paper uses an entanglement-entropy-based bound together with empirical fits for the specific product initial state |0^n> to esti

Load-bearing premise

The quantum resource counts depend on the empirical |0^n> Trotter-step fits being extrapolated reliably from small systems to n = 100; if entanglement does not suppress Trotter error that strongly at larger sizes, or if the imported O(|θ|p^2) rotation-injection error bound degrades, the claimed two-hour runtime and the crossover both inflate dramatically.

What would settle it

Run the fourth-order Trotter circuit for the product initial state at sizes n = 30–50 against a double-precision Chebyshev reference and compare the measured l2 error with the paper's 'Emp |0^n>' fit; if the required Trotter steps track the worst-case commutator bound instead, the n = 100 resource estimates are unsupported. On the hardware side, a full surface-code cycle-level simulation of the 100-site circuit would check whether the accumulated logical error stays below the target ε with the stated code distances and RUS schedules.

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

If this is right

  • If the estimates hold, a fault-tolerant machine with about 3.7 × 10^5 physical qubits at p = 10^-3 can simulate 100-site 1D mixed-field Ising dynamics to t = 50 with 1% error in about 2 hours.
  • At p = 10^-4 the same task drops to about 3.1 × 10^4 physical qubits and a few minutes; 2D tasks drop to seconds or minutes, yielding at least an order-of-magnitude reduction in both qubit count and runtime.
  • The 1D crossover at n ≈ 18–22 implies practical quantum advantage does not require millions of qubits; the transition to faster-than-classical simulation occurs at sizes reachable by near-term fault-tolerant architectures.
  • The 2D case provides the stronger classical-hardness regime: tensor-network methods cannot bound the error below about 5% for n ≥ 20 at t = √n, whereas the quantum estimate maintains 1% accuracy.
  • The Clifford+T/magic-state-distillation route is estimated to require on the order of 10^8 physical qubits at n = 100, making rotation-state injection the quantitatively preferred engineering target for early fault-tolerant devices.

Where Pith is reading between the lines

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

  • Editorial inference: The entanglement-informed Trotter suppression is argued for generic entangled states, but the paper's headline numbers lean on empirical fits for the specific |0^n> initial state; if the same suppression transfers to other initial states and lattice geometries, the crossover could appear at comparable sizes more broadly.
  • Editorial inference: The GCAE query-depth trade-off is described for Pauli observables via block encoding; a natural extension is estimating non-local observables such as string correlators, where classical sampling is harder and the quantum advantage could set in at even smaller system sizes.
  • Editorial inference: The asymptotic claim hinges on the extrapolated Trotter-step fits, so a direct classical benchmark at intermediate sizes (n = 30–50) against quasi-exact references would sharply test the crossover without requiring a quantum computer.
  • Editorial inference: The paper notes that qLDPC or other low-overhead error-correcting codes are a future direction; if adopted, the dominant surface-code distance and ancilla overhead would shrink, potentially shifting the crossover to even lower physical-qubit counts.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper presents a full-stack resource-estimation framework for fault-tolerant simulation of mixed-field Ising dynamics, combining a new Gaussian-sampled Chebyshev amplitude estimation (GCAE) algorithm, surface-code-level rotation-state injection with claimed O(|θ|p^2) residual error, and a co-designed QEC / error-mitigation analysis. It claims that for a 100-site 1D system at ε=0.01 and physical error p=10^-3, fault-tolerant simulation takes about 2 hours with 3.7×10^5 physical qubits, while MPS simulation needs about 100 years; for p=10^-4 the resource estimates shrink by an order of magnitude. The quantum runtime is obtained from fourth-order Trotter segment counts using empirical |0^n> fits, RUS layer timings, and query/error-mitigation optimization; the classical baselines are extrapolated from MPS, PEPS, tVMC, and full state-vector benchmarks up to moderate system sizes.

Significance. If the reported crossover were correct, the paper would provide an important engineering target for early fault-tolerant quantum devices and a rigorous full-stack comparison methodology. The strengths of the manuscript include the unusually detailed resource tables, the explicit decomposition of classical errors (SVD truncation vs Trotter error), and the systematic benchmarking of MPS, PEPS, tVMC, and state-vector methods. However, the central quantitative claim cannot be reproduced from the equations and fits printed in the paper; there is a large internal inconsistency between the Trotter-step fit reported in Fig. S8 and the QEC-cycle counts in Table I, as well as an inconsistency between the abstract's '100 years' and Section IV's 'about 10^9 years'. Because the headline crossover depends directly on the Trotter segment count, this flaw undermines the main conclusion rather than being a local presentation issue.

major comments (4)
  1. [Fig. S8, Eq. (S37), Table I] There is an unresolved, load-bearing mismatch in the number of Trotter segments ν. Eq. (S37) gives T_cycle = d·ν·T_step. With p=10^-3, d=18, and Eq. (S36) evaluated with the paper's own RUS timing model (t_i=2, <k_max>≈1.4 ln n +1.54, eT_Z≈1.5 T_Z), one obtains T_step≈7×10^2 at n=100. Table I's 6.5×10^6 QEC cycles for ε=0.01 then implies ν≈5×10^2. But Fig. S8 reports the empirical |0^n> fit r∼e^{0.62 n^{1.45}} for ε=0.01, which evaluates to ∼10^213 at n=100. This is not an error-bar issue; it is a roughly two-hundred-order-of-magnitude inconsistency. If the printed fit is used, the runtime and qubit estimates become astronomical; if Table I's ν≈500 is used, the underlying extrapolation is not the one reported. The caption of Fig. 1 itself states that the |0^n> Trotter count is 'obtained via extrapolation', so this is an acknowledged weak spot that nonetheless blocks the headline result.
  2. [Abstract and Section IV] The abstract and introduction state that tensor-network approaches would require 'about 100 years' for the n=100, ε=0.01, 1D task, while Section IV (paragraph on classical fits) states that extrapolating t_run∼e^{0.44n} gives 'about 10^9 years' at n=100 for the same setting. These two claims differ by seven orders of magnitude. This is not a stylistic difference: it changes the claimed crossover from a dramatic but conceivable speedup to an effectively impossible classical baseline. The discrepancy must be resolved before the crossover claim can be evaluated.
  3. [Methods A / SI S2 B] The quantum resource optimization is built on two load-bearing imported assumptions: the error-mitigation sampling overhead grows as e^{4 p_logical}, and the rotation-state injection suppresses logical error to O(|θ|p^2) using the 1-FT construction of Ref. [57]. Neither is derived in this paper, and the second is an unpublished co-authored preprint. The paper's own Fig. 2 shows that the optimal maximum query number M—and hence the total runtime—is controlled by this error-mitigation trade-off. If the p^2 scaling or the e^{4p_logical} form does not hold for all RUS angles and wrapping operations, the optimized query budgets in Table I and the derived runtimes change substantially. The authors should either provide a self-contained derivation or state clearly that the resource estimates are conditional on the correctness of Ref. [57].
  4. [Section II / Fig. 1 caption / SI S1 C] The crossover conclusions depend on extrapolating empirical |0^n> Trotter-step fits from small system sizes to n=100 without evidence that the favorable scaling persists. The entanglement-informed bound (Eq. S20) gives an upper bound that approaches the average-case scaling only when the relevant subsystems are sufficiently entangled; no such saturation is demonstrated for the |0^n> initial state at the target times and precisions. Since the quantum runtime is polynomially sensitive to ν, and Table I cannot be reconciled with the printed fit, the paper does not currently establish a reliable quantum-side resource curve beyond the fitted range.
minor comments (4)
  1. [Section II] Typo/incomplete phrase: 'For two-dimensional (2D) systems with n, rapid entanglement growth...' appears to have a missing quantity (likely n qubits).
  2. [Section II vs Section IV] The claimed crossover location is inconsistent: Section II says the separation appears for n>30, while Section IV states the crossover lies at n≈18–22 in 1D. These could refer to different error targets, but the text does not say so.
  3. [Fig. 3(e)] The crossover of the quantum curve with the MPS curve is drawn at n≈18–22, yet the '100 years' claim is for n=100. Because the axes are log-scale and the classical extrapolation is from fits, the visual crossover and the extrapolated statement should be reconciled explicitly.
  4. [Fig. 4(e)] The legend labels 'PEPS+tVMC' and 'PEPS-SU' are not defined in the caption; the reader must infer that PEPS-SU is the simple-update method from Section IV. Please define in the caption.

Circularity Check

2 steps flagged

The headline quantum runtime and crossover numbers reduce to fitted Trotter-step scalings plus a co-authored O(p^2) injection-error import; no definitional circularity, but the central claim is fit-driven.

specific steps
  1. fitted input called prediction [Main Text Fig. 1(c) caption, p.4; SI S1C Fig. S8; SI S2C Eq. (S37); Table I / Fig. 3(e)]
    ""For the specific initial state |0>, the required number of Trotter steps is obtained via extrapolation." ... "the total number of QEC cycles for a single unitary call of U(t) is given by T^{(D)}_{cycle}=d×ν_D×T^{(D)}_{step}." ... "Emp. |0^n: r e^{0.62n^{1.45}}" (Fig. S8, ε=0.01)."

    The headline 1D runtime at n=100 (Table I: 6.5×10^6 QEC cycles, 6804 s at ε=0.01, t=n/2, p=10^-3) is obtained by inserting the empirical |0^n> Trotter-step fit into Eq. (S37). Thus the 'prediction' is an algebraic rescaling of a fitted scaling, not an independent first-principles result. The paper itself acknowledges the Trotter count is 'obtained via extrapolation' rather than a bound. Moreover, the printed fit r∼e^{0.62 n^{1.45}} evaluated at n=100 gives r∼e^492≈10^213, which is irreconcilable with Table I's implied ν≈490 (6.5×10^6 cycles with d=18 and T_step≈740); the 2-hour claim is therefore not reproducible from the reported equations unless an unreported, different Trotter-count input is used. The central resource prediction reduces by construction to the fitted Trotter input.

  2. self citation load bearing [SI S2B 'Rotation state preparation', Fig. S12]
    ""The basic idea is to apply tailored physical rotations along the support of the logical Z̄ operator ... following the partially fault-tolerant preparation scheme of Ref. [57] ... We refer the reader to Ref. [57] for further technical details regarding the physical realisation." ... "the leading logical error of the injected rotation scales quadratically as α_RUS|θ|p^2 [57].""

    The main text's central claim that 'the reduction in quantum runtime arises from our improved rotation-state injection' depends on this O(|θ|p^2) residual-error scaling, which is not derived in this manuscript. It is adopted from Ref. [57], a preprint by overlapping authors (including current author P. Zeng). The manuscript's QEC-cycle and error-mitigation estimates (e.g., Fig. S13, Eq. S37) load this imported scaling. To the extent Ref. [57] is not independently verified here, the load-bearing premise is a self-citation rather than a self-contained derivation. This is not a by-construction equivalence, but it weakens the claimed first-principles status of the resource analysis.

full rationale

The paper is not circular in the definitional sense: the resource model (T_step, QEC cycles, sampling overhead) is explicit, and the classical benchmarking against MPS/tVMC/state-vector is a legitimate extrapolation of numerical fits. However, the central quantum-side prediction is fit-driven. The advertised 2-hour/n=100 runtime is obtained by feeding the empirical |0^n> Trotter-step scaling from Fig. S8 into Eq. (S37); once the fit is chosen, the runtime is forced. The paper even labels this input as 'obtained via extrapolation' rather than a bound. The internal inconsistency between the printed empirical fit (ν∼10^213 at n=100) and Table I (ν≈490) is a correctness issue rather than circularity per se, but it reinforces that the headline number is not derivable from the reported equations. A second load-bearing import is the O(|θ|p^2) rotation-state error from the co-authored Ref. [57]; the QEC and error-mitigation estimates adopt this scaling wholesale. These are the main sources of the score. The entanglement-informed Trotter bound from Ref. [63] and the GCAE algorithm described in SI are cited external results, but they are at least concretely stated in the appendices and are not by-construction equivalent to the output. On balance, the central claim partially reduces to fitted scalings and unverified self-citations, yielding a moderate circularity score.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The crossover is defined by two fitted extrapolation families: the quantum Trotter-step counts ('Emp. |0^n', Fig. S8-S10) and the classical MPS runtime/bond-dimension fits (Fig. 3e). The enabling primitives, O(|theta|p^2) rotation-state injection and the GCAE analysis, are imported from a co-authored preprint [57] and an in-preparation companion paper [91], respectively. No new physical entities are introduced. The ledger counts these imports as part of the price the reader pays upstream, along with the hand-chosen timing parameters and the 500 ns cycle-time assumption.

free parameters (5)
  • Empirical Trotter-step scaling, 1D t = n/2, epsilon = 0.01 ('Emp. |0^n') = r ~ e^{0.62 n^1.45}
    This fit determines the QEC cycle count and hence the n = 100 runtime; the worst-case fit would give e^{0.80 n^1.55}, which is astronomically larger at n = 100.
  • RUS rounds fit <k_max> = 1.4 ln n + 1.54
    Taken from Ref. [31], controls the parallel rotation-layer time T_Z(n) in Eq. (S30); a logarithmic fit whose constant offsets matter for the resource tables.
  • Rotation-state supply time t_i = 1 (p = 10^-4), 2 (p = 10^-3)
    Hand-chosen scheduling parameters in Eq. (S33), with q ~ 10 parallel ancilla patches assumed at p = 10^-3; directly enters the QEC-clock cost.
  • QEC cycle time = 500 ns
    Hardware assumption (Methods: 'We assume a QEC cycle time of 500 ns') converting code cycles to wall-clock runtime; not defended against specific architectures.
  • Classical MPS runtime extrapolation exponents = t_run ~ e^{0.28n} (epsilon = 0.1); t_run ~ e^{0.44n} (epsilon = 0.01)
    Fit to MPS data up to n = 64 and extrapolated to n = 100 (Fig. 3e); the source of the '100 years' / '10^9 years' claims.
axioms (5)
  • domain assumption Logical error rate per QEC clock q = 0.1(100p)^{floor((d+1)/2)}
    Standard empirical surface-code formula from Refs. [41,98], used for MSD distance selection in Eq. (S56).
  • ad hoc to paper Entanglement-informed Trotter bound saturates for the |0>^n initial state
    The 'Emp. |0^n' fits (Fig. S8-S10) assume the average-case/entangled bound (Eq. S20, Ref. [63]) holds at n = 100; if the worst-case bound applied, the quantum runtime claims collapse.
  • domain assumption 1-FT rotation-state injection achieves O(|theta|p^2) residual logical error
    Imported from co-authored preprint Ref. [57] (SI S2 B); the central enabler of the reduced error-mitigation overhead and of the claimed runtime reduction.
  • ad hoc to paper Error-mitigation sampling overhead grows as e^{4 p_logical}
    Exponential overhead model stated in Methods A; it sets the optimal-maximum-query trade-off in Fig. 2(e) and the total-runtime formula.
  • standard math GCAE sample-depth trade-off M in O~(epsilon^{-1+beta}), N in O~(epsilon^{-2 beta})
    Stated in SI S1 A with the proof deferred to in-preparation Ref. [91] by overlapping authors (Z. Zhang, J. Tang, J. Sun, P. Zeng).

pith-pipeline@v1.3.0-alltime-deepseek · 50283 in / 22703 out tokens · 185322 ms · 2026-08-01T21:17:37.035904+00:00 · methodology

0 comments
read the original abstract

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

Figures

Figures reproduced from arXiv: 2607.16116 by Aditya Iyer, Alexander Yosifov, Bozhen Zhou, Daniel Serrano, Dayue Qin, Jinzhao Sun, Jue Xu, Junxiang Huang, Pan Zhang, Pei Zeng, Qi Zhao, Shreyas Sadugol, Shuo Zhou, Tianfeng Feng, Tongyang Li, Wenjun Yu, Wenzheng Dong, Xiao-Ming Zhang, Xiao Yuan, Xinzhao Wang, Xiongfeng Ma, Yantao Wu, Yiming Huang, Ying Li, You Zhou, Yuan Yao, Yuntian Gu, Zhenyu Du, Zhou You, Ziruo Wang, Zixu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Error mitigation sampling overhead for [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

230 extracted references · 15 canonical work pages

  1. [1]

    arXiv preprint arXiv:2510.26845 , year=

    Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits , author=. arXiv preprint arXiv:2510.26845 , year=

    arXiv

  2. [2]

    arXiv preprint arXiv:2510.26300 , year=

    Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation , author=. arXiv preprint arXiv:2510.26300 , year=

    arXiv

  3. [3]

    Quantum , volume =

    Preskill, John , title =. Quantum , volume =. 2018 , doi =

    2018

  4. [4]

    and Wang, Yan , title =

    Keen, Trevor and Dumitrescu, Eugene F. and Wang, Yan , title =. 2021 , eprint =

    2021

  5. [5]

    Zhang, Zixu and Tang, Jiayi and Sun, Jinzhao and Zeng, Pei , note =

  6. [6]

    Physical Review X , volume =

    Li, Ying and Benjamin, Simon C , title =. Physical Review X , volume =. 2017 , doi =

    2017

  7. [7]

    , title =

    Temme, Kristan and Bravyi, Sergey and Gambetta, Jay M. , title =. Physical Review Letters , volume =. 2017 , month =. doi:10.1103/PhysRevLett.119.180509 , publisher =

    doi:10.1103/physrevlett.119.180509 2017

  8. [8]

    Reviews of Modern Physics , volume =

    Cai, Zhenyu and Babbush, Ryan and Benjamin, Simon C and Endo, Suguru and Huggins, William J and Li, Ying and McClean, Jarrod R and O’Brien, Thomas E , title =. Reviews of Modern Physics , volume =. 2023 , doi =

    2023

  9. [9]

    , title =

    Zhao, Qi and Zhou, You and Childs, Andrew M. , title =. Nature Physics , volume =. 2025 , doi =

    2025

  10. [10]

    Science , volume =

    Zhong, Han-Sen and Wang, Hui and Deng, Yu-Hao and Chen, Ming-Cheng and Peng, Li-Chao and Luo, Yi-Han and Qin, Jian and Wu, Dian and Ding, Xing and Hu, Yi and others , title =. Science , volume =. 2020 , publisher =

    2020

  11. [11]

    Science Advances , volume =

    Bulmer, Jacob FF and Bell, Bryn A and Chadwick, Rachel S and Jones, Alex E and Moise, Diana and Rigazzi, Alessandro and Thorbecke, Jan and Haus, Utz-Uwe and Van Vaerenbergh, Thomas and Patel, Raj B and others , title =. Science Advances , volume =. 2022 , publisher =

    2022

  12. [12]

    Digital quantum magnetism on a trapped-ion quantum computer , journal =

    Haghshenas, Reza and Chertkov, Eli and Mills, Michael and Kadow, Wilhelm and Lin, S-H and Chen, Yi-Hsiang and Cade, Chris and Niesen, Ido and Begu. Digital quantum magnetism on a trapped-ion quantum computer , journal =. 2026 , publisher =

    2026

  13. [13]

    Science , volume =

    Tindall, Joseph and Mello, Antonio Francesco and Fishman, Matthew and Stoudenmire, E Miles and Sels, Dries , title =. Science , volume =. 2026 , publisher =

    2026

  14. [14]

    ACM Transactions on Quantum Computing , volume =

    Preskill, John , title =. ACM Transactions on Quantum Computing , volume =. 2025 , publisher =

    2025

  15. [15]

    2025 , eprint =

    Eisert, Jens and Preskill, John , title =. 2025 , eprint =

    2025

  16. [16]

    Nature Physics , volume =

    Oh, Changhun and Liu, Minzhao and Alexeev, Yuri and Fefferman, Bill and Jiang, Liang , title =. Nature Physics , volume =. 2024 , doi =

    2024

  17. [17]

    SIAM Journal on Computing , volume =

    Kempe, Julia and Kitaev, Alexei and Regev, Oded , title =. SIAM Journal on Computing , volume =. 2006 , publisher =

    2006

  18. [18]

    and Barends, Rami and Biswas, Rupak and Boixo, Sergio and Brandao, Fernando G

    Arute, Frank and Arya, Kunal and Babbush, Ryan and Bacon, Dave and Bardin, Joseph C. and Barends, Rami and Biswas, Rupak and Boixo, Sergio and Brandao, Fernando G. S. L. and Buell, David A. and others , title =. Nature , volume =. 2019 , doi =

    2019

  19. [19]

    and Levine, Harry and Bluvstein, Dolev and Semeghini, Giulia and Omran, Ahmed and Liu, J.-G

    Ebadi, Sepehr and Keesling, Alexander and Cain, Madelyn and Wang, Tout T. and Levine, Harry and Bluvstein, Dolev and Semeghini, Giulia and Omran, Ahmed and Liu, J.-G. and Samajdar, Rhine and others , title =. Science , volume =. 2022 , doi =

    2022

  20. [20]

    Nature Physics , volume =

    Boixo, Sergio and Isakov, Sergei V and Smelyanskiy, Vadim N and Babbush, Ryan and Ding, Nan and Jiang, Zhang and Bremner, Michael J and Martinis, John M and Neven, Hartmut , title =. Nature Physics , volume =. 2018 , publisher =

    2018

  21. [21]

    Physical Review X , volume =

    Childs, Andrew M and Su, Yuan and Tran, Minh C and Wiebe, Nathan and Zhu, Shuchen , title =. Physical Review X , volume =. 2021 , publisher =

    2021

  22. [22]

    PRX Quantum , volume =

    Lin, Lin and Tong, Yu , title =. PRX Quantum , volume =. 2022 , doi =

    2022

  23. [23]

    2024 , eprint =

    Gidney, Craig and Shutty, Noah and Jones, Cody , title =. 2024 , eprint =

    2024

  24. [24]

    2021 , eprint =

    Zeng, Pei and Sun, Jinzhao and Yuan, Xiao , title =. 2021 , eprint =

    2021

  25. [25]

    Algorithms for Quantum Simulation at Finite Energies , journal =

    Lu, Sirui and Ba. Algorithms for Quantum Simulation at Finite Energies , journal =. 2021 , doi =

    2021

  26. [26]

    Quantum , volume =

    Huo, Mingxia and Li, Ying , title =. Quantum , volume =. 2023 , doi =

    2023

  27. [27]

    Quantum , volume =

    Lin, Lin and Tong, Yu , title =. Quantum , volume =. 2020 , doi =

    2020

  28. [28]

    2026 , eprint =

    Kanasugi, Shota and Toshio, Riki and Maruyama, Kazunori and Oshima, Hirotaka , title =. 2026 , eprint =

    2026

  29. [29]

    2026 , eprint =

    Toshio, Riki and Kanasugi, Shota and Fujisaki, Jun and Oshima, Hirotaka and Sato, Shintaro and Fujii, Keisuke , title =. 2026 , eprint =

    2026

  30. [30]

    Quantum , volume =

    Chakraborty, Shantanav , title =. Quantum , volume =. 2024 , publisher =

    2024

  31. [31]

    Quantum , volume =

    Ding, Zhiyan and Li, Haoya and Lin, Lin and Ni, HongKang and Ying, Lexing and Zhang, Ruizhe , title =. Quantum , volume =. 2024 , doi =

    2024

  32. [32]

    Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision , journal =

    Wang, Guoming and Fran. Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision , journal =. 2023 , publisher =

    2023

  33. [33]

    Efficient Ground-State Energy Estimation and Certification on Early Fault-Tolerant Quantum Computers , journal =

    Wang, Guoming and Fran. Efficient Ground-State Energy Estimation and Certification on Early Fault-Tolerant Quantum Computers , journal =. 2025 , doi =

    2025

  34. [34]

    Quantum , volume =

    Lin, Lin and Tong, Yu , title =. Quantum , volume =. 2020 , publisher =

    2020

  35. [35]

    PRX Quantum , volume =

    Wang, Samson and McArdle, Sam and Berta, Mario , title =. PRX Quantum , volume =. 2024 , publisher =

    2024

  36. [36]

    Quantum , volume =

    Zhang, Ruizhe and Wang, Guoming and Johnson, Peter , title =. Quantum , volume =. 2022 , publisher =

    2022

  37. [37]

    Nature Communications , volume =

    Lee, Seunghoon and Lee, Joonho and Zhai, Huanchen and Tong, Yu and Dalzell, Alexander M and Kumar, Ashutosh and Helms, Phillip and Gray, Johnnie and Cui, Zhi-Hao and Liu, Wenyuan and others , title =. Nature Communications , volume =. 2023 , publisher =

    2023

  38. [38]

    APL Computational Physics , volume =

    Ding, Zhiyan and Dong, Yulong and Tong, Yu and Lin, Lin , title =. APL Computational Physics , volume =. 2026 , doi =

    2026

  39. [39]

    Physical Review Research , volume =

    Ding, Zhiyan and Chen, Chi-Fang and Lin, Lin , title =. Physical Review Research , volume =. 2024 , publisher =

    2024

  40. [40]

    PRX Quantum , volume =

    Ding, Zhiyan and Lin, Lin , title =. PRX Quantum , volume =. 2023 , publisher =

    2023

  41. [41]

    2022 , eprint =

    Meister, Richard and Benjamin, Simon C , title =. 2022 , eprint =

    2022

  42. [42]

    Proceedings of the 56th Annual ACM Symposium On Theory Of Computing , pages =

    Chen, Chi-Fang and Huang, Hsin-Yuan and Preskill, John and Zhou, Leo , title =. Proceedings of the 56th Annual ACM Symposium On Theory Of Computing , pages =

  43. [43]

    Physical Review A , volume =

    He, Min-Quan and Zhang, Dan-Bo and Wang, ZD , title =. Physical Review A , volume =. 2022 , publisher =

    2022

  44. [44]

    2023 , eprint =

    Cubitt, Toby S , title =. 2023 , eprint =

    2023

  45. [45]

    Quantum simulation of electronic structure with linear depth and connectivity , journal =

    Kivlichan, Ian D and McClean, Jarrod and Wiebe, Nathan and Gidney, Craig and Aspuru-Guzik, Al. Quantum simulation of electronic structure with linear depth and connectivity , journal =. 2018 , publisher =

    2018

  46. [46]

    and Gidney, Craig and Huggins, William J

    Lee, Joonho and Berry, Dominic W. and Gidney, Craig and Huggins, William J. and McClean, Jarrod R. and Wiebe, Nathan and Babbush, Ryan , title =. PRX Quantum , volume =. 2021 , doi =

    2021

  47. [47]

    Fault-tolerant quantum simulation of generalized Hubbard models , journal =

    Bay-Smidt, Andreas Juul and Klausen, Frederik Ravn and S. Fault-tolerant quantum simulation of generalized Hubbard models , journal =. 2025 , publisher =

    2025

  48. [48]

    2026 , eprint =

    Hirai, Yuga and Ikari, Shota and Ueno, Yosuke and Suzuki, Yasunari , title =. 2026 , eprint =

    2026

  49. [49]

    PRX Quantum , volume =

    Akahoshi, Yutaro and Toshio, Riki and Fujisaki, Jun and Oshima, Hirotaka and Sato, Shintaro and Fujii, Keisuke , title =. PRX Quantum , volume =. 2025 , doi =

    2025

  50. [50]

    npj Quantum Information , volume =

    Yoshioka, Nobuyuki and Okubo, Tsuyoshi and Suzuki, Yasunari and Koizumi, Yuki and Mizukami, Wataru , title =. npj Quantum Information , volume =. 2024 , doi =

    2024

  51. [51]

    Chung, Ming-Zhi and Kavaki, Ali H. Z. and Scherer, Artur and Khalid, Abdullah and Kong, Xiangzhou and Kawakubo, Toru and Anand, Namit and Dagnew, Gebremedhin A. and Webb, Zachary and Silva, Allyson and others , title =. 2026 , eprint =

    2026

  52. [52]

    Low-Depth Amplitude Estimation via Statistical Eigengap Estimation , year =

    Huang, Po-Wei and Koczor, B. Low-Depth Amplitude Estimation via Statistical Eigengap Estimation , year =. arXiv:2603.05475 , howpublished =

    Pith/arXiv arXiv

  53. [53]

    Sun, Jinzhao and Zeng, Pei and Gur, Tom and Kim, M. S. , title =. Science Advances , volume =. 2026 , doi =

    2026

  54. [54]

    2025 , eprint =

    Zeng, Pei and Zheng, Guo and Xu, Qian and Jiang, Liang , title =. 2025 , eprint =

    2025

  55. [55]

    PRX Quantum , volume =

    Akahoshi, Yutaro and Maruyama, Kazunori and Oshima, Hirotaka and Sato, Shintaro and Fujii, Keisuke , title =. PRX Quantum , volume =. 2024 , doi =

    2024

  56. [56]

    Quantum , volume =

    Ding, Zhiyan and Lin, Lin , title =. Quantum , volume =. 2023 , publisher =

    2023

  57. [57]

    Quantum Science and Technology , volume =

    Campbell, Earl T , title =. Quantum Science and Technology , volume =. 2022 , publisher =

    2022

  58. [58]

    2023 , eprint =

    Xu, Meng and Vadimov, Vasilii and Krug, Malte and Stockburger, JT and Ankerhold, J , title =. 2023 , eprint =

    2023

  59. [59]

    Nature Communications , volume =

    Lambert, Neill and Ahmed, Shahnawaz and Cirio, Mauro and Nori, Franco , title =. Nature Communications , volume =. 2019 , publisher =

    2019

  60. [60]

    Physical Review Letters , volume =

    Tamascelli, Dario and Smirne, Andrea and Huelga, Susana F and Plenio, Martin B , title =. Physical Review Letters , volume =. 2018 , publisher =

    2018

  61. [61]

    Physical Review Letters , volume =

    Huang, Zhen and Park, Gunhee and Chan, Garnet Kin and Lin, Lin , title =. Physical Review Letters , volume =. 2026 , doi =

    2026

  62. [62]

    Frontiers of Physics , volume =

    Yan, YiJing and Jin, Jinshuang and Xu, Rui-Xue and Zheng, Xiao , title =. Frontiers of Physics , volume =. 2016 , publisher =

    2016

  63. [63]

    Physical Review B , volume =

    Park, Gunhee and Huang, Zhen and Zhu, Yuanran and Yang, Chao and Chan, Garnet Kin-Lic and Lin, Lin , title =. Physical Review B , volume =. 2024 , publisher =

    2024

  64. [64]

    Journal of Chemical Physics , volume =

    Tanimura, Yoshitaka , title =. Journal of Chemical Physics , volume =. 2020 , publisher =

    2020

  65. [65]

    Physical Review Letters , volume =

    Xu, Meng and Yan, Yaming and Shi, Qiang and Ankerhold, J and Stockburger, JT , title =. Physical Review Letters , volume =. 2022 , publisher =

    2022

  66. [66]

    Journal of Chemical Physics , volume =

    Yan, YiJing , title =. Journal of Chemical Physics , volume =. 2014 , publisher =

    2014

  67. [67]

    Journal of Chemical Theory and Computation , volume =

    Guo, Yukai and Gao, Xing , title =. Journal of Chemical Theory and Computation , volume =. 2025 , publisher =

    2025

  68. [68]

    Physical Review A , volume =

    Li, Xiang and Lyu, Su-Xiang and Wang, Yao and Xu, Rui-Xue and Zheng, Xiao and Yan, YiJing , title =. Physical Review A , volume =. 2024 , publisher =

    2024

  69. [69]

    Fingerprint and universal Markovian closure of structured bosonic environments , journal =

    N. Fingerprint and universal Markovian closure of structured bosonic environments , journal =. 2022 , publisher =

    2022

  70. [70]

    Nature Physics , volume =

    Verstraete, Frank and Wolf, Michael M and Ignacio Cirac, J , title =. Nature Physics , volume =. 2009 , publisher =

    2009

  71. [71]

    Physical Review Research , volume =

    Menczel, Paul and Funo, Ken and Cirio, Mauro and Lambert, Neill and Nori, Franco , title =. Physical Review Research , volume =. 2024 , publisher =

    2024

  72. [72]

    Physical Review A , volume =

    Zhou, LK and Jin, GR and Yang, W , title =. Physical Review A , volume =. 2024 , publisher =

    2024

  73. [73]

    Journal of Chemical Theory and Computation , volume =

    Dan, Xiaohan and Geva, Eitan and Batista, Victor S , title =. Journal of Chemical Theory and Computation , volume =. 2025 , publisher =

    2025

  74. [74]

    Journal of Chemical Physics , volume =

    Li, Xiang and Su, Yu and Chen, Zi-Hao and Wang, Yao and Xu, Rui-Xue and Zheng, Xiao and Yan, YiJing , title =. Journal of Chemical Physics , volume =. 2023 , publisher =

    2023

  75. [75]

    Physical Review Letters , volume =

    Schlimgen, Anthony W and Head-Marsden, Kade and Sager, LeeAnn M and Narang, Prineha and Mazziotti, David A , title =. Physical Review Letters , volume =. 2021 , publisher =

    2021

  76. [76]

    Journal of Chemical Physics , volume =

    Song, Kai and Song, Linze and Shi, Qiang , title =. Journal of Chemical Physics , volume =. 2016 , publisher =

    2016

  77. [77]

    Physical Review A , volume =

    Gao, Xing and Ren, Jiajun and Eisfeld, Alexander and Shuai, Zhigang , title =. Physical Review A , volume =. 2022 , publisher =

    2022

  78. [78]

    Physical Review Research , volume =

    Schlimgen, Anthony W and Head-Marsden, Kade and Sager, LeeAnn M and Narang, Prineha and Mazziotti, David A , title =. Physical Review Research , volume =. 2022 , publisher =

    2022

  79. [79]

    44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) , series =

    Cleve, Richard and Wang, Chunhao , title =. 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) , series =. 2017 , publisher =

    2017

  80. [80]

    Communications in Mathematical Physics , volume =

    Li, Xiantao and Wang, Chunhao , title =. Communications in Mathematical Physics , volume =. 2023 , publisher =

    2023

Showing first 80 references.