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arxiv: 2606.26233 · v1 · pith:P3ODXZLLnew · submitted 2026-06-24 · 🪐 quant-ph · cond-mat.str-el

A fidelity metric for quantum annealing benchmarked by extreme scaling quantum Monte-Carlo simulations

Gabriel Gouraud , Miha Srdinsek , Xavier Waintal This is my paper

Pith reviewed 2026-06-26 01:44 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords quantum annealingfidelity metricquantum Monte CarloRydberg atomsequation of stateadiabatic evolutionbenchmarkingoptimization
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The pith

A fidelity metric based on equation-of-state accuracy benchmarks quantum annealing to 10^{-4} at 100,000 atoms.

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

The paper introduces an equation-of-state accuracy metric ε as a fidelity measure for the quantum annealing process itself. This quantity assesses how closely the annealer follows the ground-state evolution during Hamiltonian interpolation, independent of any particular optimization problem or classical solver. Two quantum Monte Carlo methods are used to compute benchmark values of ε for Rydberg atom systems: a variational approach with thermal-annealing ansatz reaches 10^{-2} to 10^{-3} up to 100 million atoms, while Green-function Monte Carlo reaches around 10^{-4} up to 100 thousand atoms. These simulated benchmarks exceed the precision and scale of existing Rydberg experiments by orders of magnitude and indicate when a quantum annealer becomes indistinguishable from a classical thermal counterpart.

Core claim

The authors define ε as the accuracy with which the annealer reproduces the equation of state of the system as the Hamiltonian interpolates from trivial to non-trivial. Variational quantum Monte-Carlo simulations with a thermal-annealing ansatz establish that ε ∼ 10^{-2}−10^{-3} suffices to make the quantum process indistinguishable from classical thermal annealing, with this precision attained at system sizes of 100,000,000 atoms on a single CPU. Green-function quantum Monte-Carlo improves the accuracy to ε ∼ 10^{-4} at 100,000 atoms. The resulting values serve as reference benchmarks that current experimental Rydberg platforms do not yet reach.

What carries the argument

The fidelity metric ε, defined as the accuracy of the annealer's equation of state during Hamiltonian interpolation.

If this is right

  • The metric evaluates the annealing process quality rather than final optimization success and remains independent of the chosen problem instance or classical reference algorithm.
  • Variational quantum Monte-Carlo reaches ε of order 10^{-2} to 10^{-3} at 100 million atoms on one CPU.
  • Green-function quantum Monte-Carlo reaches ε around 10^{-4} at 100 thousand atoms.
  • The benchmark values impose concrete precision and size targets that future quantum annealing hardware must meet or surpass.
  • Existing Rydberg-atom experimental platforms are outperformed by the simulated benchmarks in both precision and system size by orders of magnitude.

Where Pith is reading between the lines

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

  • Adoption of ε would allow direct numerical comparison of fidelity across different quantum annealing hardware platforms.
  • The same simulation methods could be used to predict the minimal hardware improvements needed to exceed classical thermal performance at a chosen ε.
  • The metric opens a route to unify benchmarking language between quantum annealing and gate-based quantum computing by treating ε as an analogue of fidelity per gate.
  • If real devices match the Monte Carlo predictions at the reported precisions, it would confirm that current experimental limitations are mainly technical rather than fundamental.

Load-bearing premise

The two quantum Monte Carlo techniques faithfully reproduce the dynamics and equation of state that would occur in a real experimental quantum annealer.

What would settle it

An experimental Rydberg-atom device that measures its own equation of state during annealing and finds a systematic deviation from the Monte Carlo predictions larger than the reported ε at comparable system sizes.

Figures

Figures reproduced from arXiv: 2606.26233 by Gabriel Gouraud, Miha Srdinsek, Xavier Waintal.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sketch of the Rydberg atom phase diagrams for [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ). Perturbation theory in hx for Hˆ = Hˆ z − hxHˆ x gives E0 = F(n˜) − h 2 x X i 1 δi + O(h 3 x ), (C1) with δi defined as δi = Jii + 2(1 − 2˜ni) X j Jijn˜j . (C2) 2. Strong field expansion (hx ≫ Jij ) At large field, the reference state is the ground state of Hˆ x, i.e., |+⟩ ⊗N . Apply perturbation theory to H/h ˆ x = Hˆ x − 1 hx Hˆ z. The perturbation Hˆ z contains terms acting on either one site ˆni or … view at source ↗
Figure 12
Figure 12. Figure 12: shows our gap estimate for the fallen angel QUBO problem of [63]. As advertised, we do observe a gap closing that takes place at vanishing (or at least very small) transverse field hx. All of the 5 individual QUBO instances we had access to had similar gap profiles. Appendix E: Variance scaling and V-score In this appendix, we briefly discuss the variance of the energy σ 2 , σ 2 ≡ ⟨ψV|Hˆ 2 |ψV⟩ ⟨ψV|ψV⟩ − … view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 3
Figure 3. Figure 3: The top panel of Fig. 14 shows the difference in [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: shows a calculation with the staggered thermal ansatz where we have performed a standard annealing (slowly decreasing hx, optimizing the effective temper￾atures at every step) as well as a backward-annealing (slowly increasing hx, also optimizing the effective tem￾peratures at every step). For the square lattice, the stag￾gered magnetization shows no hysteresis and a M(hx) curve consistent with a second o… view at source ↗
read the original abstract

Quantum annealers are supposed to follow adiabatically the ground state of a system as its Hamiltonian slowly interpolates between a trivial phase and a non-trivial one; the non-trivial ground state being the solution to an optimization problem. Overwhelmingly, their performances are measured in terms of how well or fast the optimization problem is solved. While pragmatic, this approach is inherently brittle as it strongly depends on the problem considered and the classical algorithm used as the reference benchmark. Here, we propose a quantity that not only measures the end result but also the quality of the actual quantum annealing process itself. Our metric is the quantum annealing counterpart of the fidelity-per gate of gate-based quantum computers. It takes the form of an accuracy $\epsilon$ for the equation of state of the annealer. We calculate benchmark values of $\epsilon$ using two variants of the simulated quantum annealing technique for Rydberg atoms systems. Our first approach uses variational quantum Monte-Carlo with an ansatz inspired by thermal annealing. It suggests that within $\epsilon \sim 10^{-2}-10^{-3}$, a quantum annealer is indistinguishable from its thermal classical counterpart. Critically, we could reach this precision up to $100,000,000$ atoms on a single CPU. Our second approach (based on Green function quantum Monte-Carlo) reaches accuracies around $\epsilon \sim 10^{-4}$ and we have run it up to $100,000$ atoms. These results outperform current Rydberg atom quantum annealing experimental platforms in both precision and size by orders of magnitude and put severe constraints for future hardware.

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 / 1 minor

Summary. The paper introduces a fidelity metric ε for quantum annealing, defined as the accuracy with which the annealer reproduces the equation of state during the annealing process (analogous to fidelity per gate in gate-based QC). It benchmarks ε for Rydberg-atom systems using two simulated quantum annealing methods: variational quantum Monte Carlo with a thermal-annealing ansatz (reaching ε ∼ 10^{-2}–10^{-3} up to 10^8 atoms) and Green-function QMC (reaching ε ∼ 10^{-4} up to 10^5 atoms). The central claim is that these benchmark values already outperform current Rydberg experimental platforms by orders of magnitude in both precision and size, thereby imposing severe constraints on future hardware.

Significance. If the QMC simulations are shown to faithfully reproduce the relevant observables of actual quantum annealing dynamics, the proposed ε metric would offer a problem-independent figure of merit that directly quantifies annealing quality rather than end-point success. The reported extreme scaling (single-CPU runs to 10^8 atoms) demonstrates a clear computational advantage over direct experimental characterization and could serve as a useful reference once the proxy assumption is validated.

major comments (2)
  1. [Abstract] Abstract: the claim that the computed ε values 'outperform current Rydberg atom quantum annealing experimental platforms … and put severe constraints for future hardware' rests on the unverified assumption that the variational thermal-annealing QMC and Green-function QMC produce the same instantaneous or time-averaged observables that an ideal experimental device would produce under the same schedule. No small-system validation against exact time-dependent Schrödinger evolution or against published Rydberg annealing data is referenced, rendering the hardware-constraint conclusion unsupported.
  2. [Abstract] Abstract: the variational ansatz is explicitly constructed from a classical thermal distribution, yet the paper asserts it benchmarks quantum annealing; without a demonstration that it reproduces coherent or non-adiabatic quantum evolution (as opposed to classical thermal sampling), the reported ε ∼ 10^{-3} cannot be interpreted as a quantum-fidelity benchmark.
minor comments (1)
  1. [Abstract] The abstract does not define the precise functional form of ε or the equation of state being matched; a short explicit definition would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on the manuscript. We address each major comment below, clarifying the scope of our QMC benchmarks and proposing targeted revisions to the abstract and main text.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the computed ε values 'outperform current Rydberg atom quantum annealing experimental platforms … and put severe constraints for future hardware' rests on the unverified assumption that the variational thermal-annealing QMC and Green-function QMC produce the same instantaneous or time-averaged observables that an ideal experimental device would produce under the same schedule. No small-system validation against exact time-dependent Schrödinger evolution or against published Rydberg annealing data is referenced, rendering the hardware-constraint conclusion unsupported.

    Authors: We acknowledge that the manuscript does not include explicit small-system benchmarks against exact time-dependent Schrödinger evolution or direct comparison to published Rydberg annealing experiments. The Green-function QMC is a standard projector method capable of simulating quantum dynamics under a time-dependent schedule, while the variational thermal-annealing ansatz is introduced specifically to establish a classical reference. The hardware-constraint statement is therefore framed relative to these simulated proxies rather than a fully validated ideal quantum annealer. We will revise the abstract to qualify the claim as applying to the simulated ideal case and add a brief discussion of the proxy assumptions together with relevant literature on QMC validation for Rydberg systems. revision: partial

  2. Referee: [Abstract] Abstract: the variational ansatz is explicitly constructed from a classical thermal distribution, yet the paper asserts it benchmarks quantum annealing; without a demonstration that it reproduces coherent or non-adiabatic quantum evolution (as opposed to classical thermal sampling), the reported ε ∼ 10^{-3} cannot be interpreted as a quantum-fidelity benchmark.

    Authors: The manuscript text already states that the variational QMC results indicate a quantum annealer would be 'indistinguishable from its thermal classical counterpart' within ε ∼ 10^{-2}–10^{-3}. This method is presented as one of two variants to furnish a classical thermal baseline, while the Green-function QMC supplies the higher-accuracy quantum benchmark (ε ∼ 10^{-4}). We will revise the abstract and relevant sections to make this distinction explicit and to avoid any implication that the variational ε value constitutes a quantum-fidelity benchmark. revision: yes

Circularity Check

0 steps flagged

No circularity; metric defined independently and benchmarks computed via external Monte Carlo methods

full rationale

The paper defines the fidelity metric ε directly as an accuracy measure on the equation of state of the annealing process, independent of any simulation output. Benchmark values of ε are then obtained by running two separate QMC algorithms (variational with thermal ansatz, and Green-function) on the target Rydberg systems. No equation or result is shown to be equivalent to its inputs by construction, no parameter is fitted to a subset and relabeled as a prediction, and no load-bearing claim reduces to a self-citation. The derivation chain therefore remains self-contained against the supplied simulation procedures.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; ε is introduced as a new accuracy measure without detailing its functional form or underlying assumptions.

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