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arxiv: 2606.20551 · v1 · pith:L2IVUGCXnew · submitted 2026-06-18 · 🪐 quant-ph

Benchmark of quantum algorithms for ground state preparation in the presence of noise

Daniel Molpeceres , Sirui Lu , J. Ignacio Cirac , Barbara Kraus This is my paper

Pith reviewed 2026-06-26 16:54 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum algorithmsground state preparationnoiseadiabatic evolutioncooling algorithmstopological phasequantum phase transitiondepolarizing noise
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The pith

Adiabatic evolution prepares ground states better in trivial phases of noisy fermionic systems, while multi-frequency cooling is superior in topological phases.

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

The paper benchmarks cooling, adiabatic, and optimization algorithms for preparing ground states on quantum computers when noise is present. It uses a solvable model of quadratic fermions with depolarizing noise that has a phase transition between trivial and topological regimes. Adiabatic methods work well away from the transition but suffer when the gap closes in the topological phase. Cooling algorithms handle the topological case better and are more robust to imperfect parameters. This helps decide which algorithm to use for noisy quantum hardware depending on the system's phase.

Core claim

Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, the authors show that the performance of ground-state preparation algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. The cooling protocol also shows enhanced robustness to parameter imperfections.

What carries the argument

Exactly solvable quadratic fermionic Hamiltonians with depolarizing noise, used to derive scaling of relative energy with noise rate for comparing adiabatic, cooling, and QAOA algorithms across trivial and topological phases.

If this is right

  • Adiabatic protocols should be preferred for ground state preparation in trivial phases of noisy systems.
  • Multi-frequency cooling algorithms offer better performance near quantum phase transitions in topological phases.
  • QAOA performs similarly to cooling in trivial phases but lags in topological regimes.
  • Cooling methods maintain advantage under parameter imperfections in this model.

Where Pith is reading between the lines

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

  • These benchmarks could guide algorithm selection for other noisy many-body systems beyond fermions.
  • Future hardware tests might compare these algorithms on actual quantum devices using similar phase diagrams.
  • Extensions to interacting Hamiltonians could reveal if the phase-dependent ranking persists.

Load-bearing premise

The exactly solvable family of quadratic fermionic Hamiltonians with depolarizing noise represents general noisy quantum systems well enough to rank preparation algorithms.

What would settle it

A numerical or experimental demonstration that adiabatic methods outperform cooling in the topological phase of a different noisy Hamiltonian would falsify the ranking.

Figures

Figures reproduced from arXiv: 2606.20551 by Barbara Kraus, Daniel Molpeceres, J. Ignacio Cirac, Sirui Lu.

Figure 1
Figure 1. Figure 1: FIG. 1. Difference [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Difference [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Individual cooling rates [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Optimal relative energy [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Optimal relative energy [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the optimal relative energies as three￾dimensional surface plots over the (θ/π, log10 κ) plane for N = 20 sites. Both surfaces decrease (i.e., improve) as κ decreases and as θ approaches π/2. The main difference arises near θ = 0 (topological phase). There, QAOA faces limitations, which might be related to the SPT depth constraint mentioned above, whereas cooling attains lower energies. In the trivia… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Rescaled averaged cooling rate [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Relative energy [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Relative energy [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Optimal relative energy [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: illustrates the effect of noise on the adiabatic evolution targeting θf = π/3 (within the trivial phase, no gap closing). It shows that the analytical predictions accurately capture both the scaling behavior and the po￾sition of these minima. For short T, the energy decreases as T −2 and is dominated by non-adiabatic excitations present even in the absence of noise. For large T, depo￾larization effects be… view at source ↗
read the original abstract

We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise. Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, we derive the scaling of the achievable relative energy as a function of the noise rate and support these results with numerical simulations. The Hamiltonian exhibits two phases, separated by a quantum phase transition. As expected, the performance of the different algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm, as proposed in [1], becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. We further present numerical results for the quantum approximate optimization algorithm [2], showing that it performs competitively with cooling in the trivial phase but is typically outperformed in the topological regime. Finally, we show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections, highlighting its potential advantage for realistic implementations of noisy quantum state preparation. The analytical approach developed here, in conjunction with numerical validation, establishes an extendable approach to benchmarking ground-state preparation algorithms.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript compares cooling, adiabatic, and optimization algorithms for ground-state preparation under noise. Using an exactly solvable family of quadratic fermionic Hamiltonians with depolarizing noise, the authors derive scaling laws for relative energy versus noise rate, supported by numerics. The model has trivial and topological phases separated by a quantum phase transition. Adiabatic evolution is favorable in the trivial phase; a multi-frequency cooling algorithm is competitive or superior in the topological phase due to gap closing. QAOA is competitive in the trivial phase but typically outperformed in the topological regime. Cooling shows enhanced robustness to parameter imperfections. The work frames the analytical approach as an extendable benchmarking method.

Significance. If the results hold, the exact solvability enabling derivation of scaling laws (supported by numerics) is a clear strength, providing concrete, non-fitted predictions for this model class. The phase-dependent performance comparison and the robustness result for cooling are useful insights for noisy state preparation. The extendable benchmarking framing could template similar studies, though its scope remains to be demonstrated.

major comments (1)
  1. [Abstract] Abstract: the positioning of the work as establishing an 'extendable approach to benchmarking' is load-bearing for the paper's framing, yet the manuscript provides no concrete argument, example, or evidence that the phase-dependent ranking or robustness properties extend beyond quadratic fermionic Hamiltonians and depolarizing noise.
minor comments (1)
  1. The abstract references [1] and [2] without full bibliographic details; ensure these are expanded in the reference list.

Simulated Author's Rebuttal

1 responses · 0 unresolved

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

read point-by-point responses

  1. Referee: [Abstract] Abstract: the positioning of the work as establishing an 'extendable approach to benchmarking' is load-bearing for the paper's framing, yet the manuscript provides no concrete argument, example, or evidence that the phase-dependent ranking or robustness properties extend beyond quadratic fermionic Hamiltonians and depolarizing noise.

    Authors: We agree that the manuscript contains no explicit demonstrations, examples, or arguments showing that the observed phase-dependent rankings or the robustness advantage of cooling extend to Hamiltonians outside the quadratic fermionic class or to noise models other than depolarizing. The phrasing in the abstract and conclusion frames the analytical method (exact solvability plus noise-channel analysis) as potentially reusable, but this is an aspirational statement rather than a substantiated claim. To address the concern directly, we will revise the abstract and the final paragraph of the conclusion to remove the implication that the specific performance ordering or robustness result is already shown to be general, and instead state that the present work supplies an exactly solvable benchmark for this model family while the broader applicability of the method remains to be explored in future studies. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are model-driven and independent

full rationale

The paper analytically derives relative-energy scalings from the closed-form spectrum of an exactly solvable quadratic fermionic Hamiltonian under depolarizing noise, then numerically validates algorithm performance on the same model. Phase-dependent rankings (adiabatic vs. multi-frequency cooling) follow directly from the model's gap-closing behavior at the quantum phase transition; no fitted parameters are relabeled as predictions, no self-citation chain supplies the central result, and the model is chosen precisely because its solvability permits exact comparison independent of the algorithms. The representativeness claim is presented as an 'extendable approach' rather than a derived theorem, so the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the model is presented as exactly solvable quadratic fermionic Hamiltonians under depolarizing noise, treated as a domain assumption rather than derived.

axioms (1)
  • domain assumption Depolarizing noise acts uniformly on the quadratic fermionic system and preserves the exact solvability
    This noise model is chosen to enable closed-form scaling derivations (abstract).

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Reference graph

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    In order to choose those quantities, we note that in the weak coupling limit the cooling rate as a function of the mode energy ϵk is given by a Lorentzian function centered at ∆ and with a linewidth γ0 ∝ 1/t (see Eq. (A27) and Fig. 3). That is, if we choose one particular ∆ it will cool down the modes k with ϵk around the interval ∆ ±γ 0. Thus, we have to...

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