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arxiv: 2605.04025 · v1 · submitted 2026-05-05 · 🪐 quant-ph

Recognition: unknown

Fast, accurate, high-resolution simulation of large-scale Fermi-Hubbard models on a digital quantum processor

Gavin S. Hartnett , Khadijeh Sona Najafi , Aleksei Khindanov , Haoran Liao , Michael Schutzman , Michael R. Hush , Michael J. Biercuk , Yuval Baum
Authors on Pith no claims yet

Pith reviewed 2026-05-07 03:45 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Fermi-Hubbard modeldigital quantum simulationspin-charge separationTrotter evolutionTDVPsuperconducting qubitsmany-body physicsquantum advantage
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The pith

Digital quantum processors can accurately simulate the one-dimensional Fermi-Hubbard model using up to 120 qubits and outperform classical methods in speed for long evolution times.

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

The paper demonstrates experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting processor at scales up to 120 qubits. An efficient mapping reduces circuit complexity while error suppression enables up to 90 Trotter steps of evolution. From a vacancy in a 62-qubit Néel state, spin-charge separation is observed to t=9 and velocity ratios match classical simulations. At 120 qubits, results agree with TDVP classical simulations within about 1% RMSE up to t=6, but the quantum device runs up to 3000 times faster at the limit of agreement. Readers would care because this shows quantum hardware becoming competitive for studying complex fermionic dynamics where classical tensor-network methods slow down considerably.

Core claim

We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art tensor-network methods. We encode this problem using up to 120 qubits through an efficient mapping that reduces circuit complexity, and we improve accuracy through error suppression to simulate dynamical evolution using up to 90 Trotter steps. From a vacancy defect introduced in the middle of an L=31-site (62-qubit) Néel initial state, we directly observe spin-charge separation to t=9 in natural units using up to 90 Trotter steps, and quantitatively extract velocity

What carries the argument

Efficient mapping of the Fermi-Hubbard model to qubits that reduces circuit complexity, paired with overhead-free error-suppression techniques for accurate Trotterized time evolution.

If this is right

  • Direct observation of spin-charge separation in 62-qubit systems with velocity ratios matching classical calculations.
  • Quantitative agreement with TDVP at RMSE ~1% for t up to ~5 in natural units at 120 qubits.
  • Wall-clock speedups of up to 3000x compared to optimized TDVP with bond dimension 4096.
  • Enables study of fermionic many-body dynamics in regimes where classical methods are prohibitively expensive.

Where Pith is reading between the lines

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

  • This could extend to simulating two-dimensional Fermi-Hubbard models relevant to superconductivity research.
  • Hardware scaling might allow longer accurate evolution times or larger lattices in the future.
  • The methods could apply to other interacting fermion systems for faster dynamical studies.
  • Quantum devices may become preferred for validating classical approximations in complex quantum dynamics.

Load-bearing premise

The mapping and error-suppression keep quantum errors low enough for quantitative agreement with TDVP at 120 qubits and t greater than or equal to 5 without uncharacterized biases or selective post-processing.

What would settle it

A calculation or experiment revealing that the quantum-measured spin-charge separation velocities or site densities deviate from independent high-accuracy classical results at the same parameters would falsify the quantitative accuracy.

Figures

Figures reproduced from arXiv: 2605.04025 by Aleksei Khindanov, Gavin S. Hartnett, Haoran Liao, Khadijeh Sona Najafi, Michael J. Biercuk, Michael R. Hush, Michael Schutzman, Yuval Baum.

Figure 1
Figure 1. Figure 1: Application-aware compilation for fermionic simulation. (a) The fermion-to-spin mapping represents a length-L chain of sites with L = 8 here (top row, purple circles) as a system of 2L qubits, one for each site/spin combination (bottom row, red and blue circles). We use a pair-interleaved ordering ↓↑↑↓↓↑↑↓ · · · . The nearest-neighbor hopping interactions (indicated by the ↔ arrows in the top row) map to “… view at source ↗
Figure 2
Figure 2. Figure 2: Spin-charge separation exhibited in the evolution of a central vacancy in a N´eel initial state for L = 31 over a range of repulsive couplings in each column (U > 0). All simulations run to a total time t = 9 t −1 h . Simulations in panels (a,d) use 45 Trotter steps, (b,e) use 60 Trotter steps, and (c,f) use 90 Trotter steps. (a–c) Heatmaps of the charge tracer correlator C c i (t) := ⟨ni,↑(t) + ni,↓(t)⟩ −… view at source ↗
Figure 3
Figure 3. Figure 3: Digital quantum simulation of the Fermi-Hubbard model for two initial states of an L = 60 chain with interaction strength U/th = −2: a N´eel state (left) and a N´eel state with a central vacancy defect (right). (a) Heatmap showing the evolution of the per-site spin-up occupation ⟨ni,↑⟩. To enhance the visibility of small late-time occupations, the colormap applies the transformation σ(⟨ni,↑⟩), where σ(x) =… view at source ↗
Figure 4
Figure 4. Figure 4: Quantum simulator outputs benchmarked against TDVP for a range of bond dimensions, χ ∈ {64, 128, 256, 512, 1024, 2048, 4096}. (a) Time evolution of the occupation expectation value of a representative spin-orbital, ⟨n46,↑⟩(t) for site i = 46. Quantum hardware results are shown as purple circles; TDVP results are shown as solid lines, with color indicating bond dimension χ. The light rectangu￾lar box indica… view at source ↗
read the original abstract

We report experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at a scale beyond the reach of exact statevector simulation and challenging for state-of-the-art tensor-network methods. We encode this problem using up to 120 qubits through an efficient mapping that reduces circuit complexity, and we improve accuracy through error suppression to simulate dynamical evolution using up to 90 Trotter steps. From a vacancy defect introduced in the middle of an $L=31$-site (62-qubit) N\'{e}el initial state, we directly observe spin-charge separation to $t=9$ in natural units using up to 90 Trotter steps, and quantitatively extract velocity ratios $v_c/v_s$ which match classical simulations across a range of model parameters. We then extend experiments to $L=60$ (120 qubits) and long evolution times to $t=6$ using 30 Trotter steps; Quantum-processor outputs agree quantitatively with approximate classical simulations performed using a time-dependent variational principle (TDVP) solver; increasing the TDVP bond dimension through $\chi = 4096$ expands the range of evolution times within which agreement has RMSE $\sim 1\%$ before the approaches diverge. Owing to the large scale of the simulation and the use of efficient overhead-free error-suppression techniques, for simulated evolution times at the limit of quantum/classical agreement ($t\gtrsim 5$ in natural hopping units), the wall-clock runtime of the quantum processor is up to $3000\times$ faster than an optimized TDVP simulation using $\chi = 4096$. These results establish contemporary digital quantum processors as a versatile, quantitatively accurate, and competitive platform for the study of fermionic many-body dynamics in regimes where leading classical methods can become prohibitively expensive.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript reports experimental digital quantum simulation of the one-dimensional Fermi-Hubbard model on a superconducting quantum processor at scales up to 120 qubits. Using an efficient fermionic mapping and overhead-free error suppression, the authors perform Trotterized real-time evolution (up to 90 steps on 62 qubits and 30 steps on 120 qubits). They directly observe spin-charge separation from a vacancy defect in an L=31 Néel state to t=9, extract velocity ratios v_c/v_s that match classical simulations across U/t values, and demonstrate quantitative agreement (RMSE ~1%) with TDVP tensor-network simulations for the L=60 system up to t=6, while reporting wall-clock speedups up to 3000× relative to optimized TDVP at χ=4096.

Significance. If the accuracy claims hold, the work would establish digital quantum processors as a practical platform for fermionic many-body dynamics in regimes where exact classical simulation is impossible and approximate tensor-network methods become expensive. The direct observation of spin-charge separation at 62 qubits, the parameter-scan validation of velocity ratios, and the reported runtime advantage constitute concrete progress toward quantum utility in condensed-matter simulation. The efficient mapping and error-suppression approach are technical strengths that enable the reported scale.

major comments (2)
  1. [L=60 results] L=60 (120-qubit) results section: The central claim of quantitative accuracy (RMSE ~1% agreement with TDVP at χ=4096 for t≳5) is load-bearing for the assertion that the quantum processor produces faithful dynamics. However, the manuscript provides no Trotter-step convergence data, no independent characterization of residual hardware errors after suppression, and no comparison against higher-χ TDVP or alternative classical methods. Because TDVP at finite χ is itself approximate, any uncharacterized device bias that happens to track the TDVP trajectory would be invisible in the presented comparison, leaving the quantitative-accuracy claim unsubstantiated at the largest scales.
  2. [L=31 results] Spin-charge separation and velocity-ratio extraction (L=31 experiments): The reported match of v_c/v_s across U/t is presented as external validation, yet the manuscript does not detail the precise procedure for locating charge and spin fronts from the measured density profiles, nor does it report uncertainties or sensitivity to post-selection cuts. This weakens the evidential weight of the velocity-ratio agreement for the overall accuracy narrative.
minor comments (3)
  1. [Abstract and introduction] The abstract and main text refer to evolution “in natural units” without an explicit statement that the hopping t sets the unit of time; a single clarifying sentence would remove ambiguity for readers outside the immediate subfield.
  2. [Figures] Figure captions for the density-profile plots should state the number of experimental shots and any post-selection fraction applied, to allow readers to assess statistical precision directly.
  3. [Discussion] The wall-clock runtime comparison (3000×) is given for t≳5; a brief table or sentence specifying the classical hardware, TDVP implementation details, and exact wall-clock numbers used would strengthen the speedup claim.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for the careful and constructive review. The comments identify important areas where additional detail and clarification will strengthen the manuscript. We address each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: L=60 results: The central claim of quantitative accuracy (RMSE ~1% agreement with TDVP at χ=4096 for t≳5) is load-bearing. However, the manuscript provides no Trotter-step convergence data, no independent characterization of residual hardware errors after suppression, and no comparison against higher-χ TDVP or alternative classical methods. Because TDVP at finite χ is itself approximate, any uncharacterized device bias that happens to track the TDVP trajectory would be invisible, leaving the quantitative-accuracy claim unsubstantiated at the largest scales.

    Authors: We agree that these elements are important for substantiating the accuracy claim at the largest scale. In the revised manuscript we have added Trotter-step convergence data for the L=60 system, confirming that the chosen step size yields results stable within the reported RMSE. We have also expanded the supplementary material with additional validation of the error-suppression technique on smaller systems where exact classical comparisons are possible. For higher-χ TDVP, χ=4096 is the practical limit of our classical resources for the relevant evolution times; we have clarified the text to state that the reported agreement is with the highest-χ TDVP accessible to us and that the observed divergence beyond t≈6 is consistent with the expected breakdown of finite-χ TDVP. While we acknowledge that this does not constitute a comparison to an exact method (intractable at this scale), the consistency with smaller-system benchmarks and the parameter dependence of the velocity ratios provide supporting evidence. We have added an explicit discussion of these limitations. revision: partial

  2. Referee: Spin-charge separation and velocity-ratio extraction (L=31 experiments): The reported match of v_c/v_s across U/t is presented as external validation, yet the manuscript does not detail the precise procedure for locating charge and spin fronts from the measured density profiles, nor does it report uncertainties or sensitivity to post-selection cuts. This weakens the evidential weight of the velocity-ratio agreement.

    Authors: We agree that greater transparency in the analysis procedure will improve the evidential strength. In the revised manuscript we have added a detailed description of the front-location procedure, including the fitting functions and identification criteria applied to the measured density profiles. We now also report uncertainties obtained via bootstrap resampling of the experimental shots and include a sensitivity analysis demonstrating that the extracted v_c/v_s ratios remain stable across a range of post-selection thresholds. These additions appear in the main text with further details in the supplementary information. revision: yes

standing simulated objections not resolved
  • Independent full characterization of residual hardware errors after suppression specifically for the L=60 system (beyond smaller-system validations).
  • Direct comparison to TDVP with bond dimension χ > 4096 (prohibitively expensive with available classical resources).

Circularity Check

0 steps flagged

No significant circularity; results are independent experimental data benchmarked against separate classical TDVP simulations.

full rationale

The paper's core claims rest on direct hardware measurements of Fermi-Hubbard dynamics (spin-charge separation at L=31, velocity ratios, and quantitative agreement at L=60 up to t=6) obtained via Trotterized circuits with error suppression. These outputs are compared to independent TDVP runs at varying bond dimensions without parameter fitting or redefinition of observables to match the classical solver. No equations or steps reduce the reported experimental quantities to the TDVP results by construction, and no load-bearing self-citations or ansatzes are invoked to force the agreement. The mapping and suppression techniques are applied to generate the data, but the data themselves remain externally falsifiable against the classical benchmark. This is the standard case of an experimental result validated by an independent method.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The simulation rests on established quantum mechanics and standard numerical approximations. Free parameters are physical model inputs and simulation hyperparameters. No new physical entities are postulated.

free parameters (2)
  • interaction-to-hopping ratio U/t
    Physical parameter varied across experiments to test different regimes of the Fermi-Hubbard model.
  • number of Trotter steps
    Simulation hyperparameter selected up to 90 to balance accuracy against circuit depth and accumulated error.
axioms (2)
  • standard math Trotter-Suzuki product formula approximates continuous time evolution of the Hamiltonian
    Basis for implementing digital quantum simulation of the continuous-time dynamics.
  • domain assumption Error-suppression techniques sufficiently mitigate hardware noise for the reported evolution depths
    Required to support the claim of quantitative accuracy at 90 Trotter steps on 120 qubits.

pith-pipeline@v0.9.0 · 10444 in / 1507 out tokens · 187364 ms · 2026-05-07T03:45:19.922053+00:00 · methodology

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