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arxiv: 2409.13587 · v2 · submitted 2024-09-20 · 🪐 quant-ph · cs.SE

Accelerating Quantum Eigensolver Algorithms With Machine Learning

Avner Bensoussan , Elena Chachkarova , Karine Even-Mendoza , Sophie Fortz , Connor Lenihan This is my paper

Pith reviewed 2026-05-23 20:09 UTC · model grok-4.3

classification 🪐 quant-ph cs.SE
keywords quantum eigensolvermachine learninghyperparameter optimizationNISQ devicesground state energyXGBoostquantum algorithms
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0 comments X

The pith

Machine learning models trained on up to 16-qubit data predict hyperparameters that cut error by 0.12% on 28-qubit quantum eigensolver calculations.

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

The paper tries to establish that machine learning can accelerate ground-state energy calculations on NISQ devices by predicting effective hyperparameters for quantum eigensolver algorithms. Small XGBoost regressors were trained on classically mined data from systems of at most 16 qubits and then used to set hyperparameters for 20-, 24-, and 28-qubit instances. A sympathetic reader would care because fewer manual trials would be needed to obtain usable results from near-term quantum hardware. The reported outcome is a modest error reduction on the largest tested systems, while results on the intermediate sizes remain inconclusive and call for closer attention to Hamiltonian features in the training set.

Core claim

The authors state that two small XGBoost regressor models, trained on classically mined data from systems with up to 16 qubits, predict hyperparameter values for the Quantum Eigensolver that produce a 0.12% reduction in error on 28-qubit systems; results on 20- and 24-qubit systems were inconclusive, leading to the suggestion that training data selection should be refined according to Hamiltonian characteristics.

What carries the argument

XGBoost Python regressor models that map features from small-system Hamiltonian data to hyperparameter values for larger Quantum Eigensolver runs.

If this is right

  • Hyperparameter prediction via the trained models produces a measurable drop in error for ground-state energy estimates on 28-qubit Hamiltonians.
  • Data collected from systems no larger than 16 qubits is treated as sufficient to guide optimization on systems up to 28 qubits.
  • Inconclusive performance on 20- and 24-qubit cases indicates that Hamiltonian characteristics must be taken into account when selecting or augmenting the training set.
  • The same modeling approach is proposed for optimizing other subroutines of quantum algorithm execution besides hyperparameter choice.

Where Pith is reading between the lines

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

  • If the generalization holds, manual tuning effort for variational quantum algorithms on NISQ hardware could shrink substantially.
  • The technique could be tested on other variational methods whose performance also depends on a small set of continuous hyperparameters.
  • Expanding the training corpus to include a wider range of Hamiltonian structures would provide a direct check on whether the observed 0.12% gain persists or improves.

Load-bearing premise

Models trained on classically mined data from systems with up to 16 qubits can generalize to predict effective hyperparameters for 20-, 24-, and 28-qubit systems.

What would settle it

Applying the predicted hyperparameters to 28-qubit systems and observing no error reduction (or an increase) relative to untuned runs would falsify the central performance claim.

Figures

Figures reproduced from arXiv: 2409.13587 by Avner Bensoussan, Connor Lenihan, Elena Chachkarova, Karine Even-Mendoza, Sophie Fortz.

Figure 1
Figure 1. Figure 1: QCELS circuit [19]. 3 |ck⟩ is a state corresponding to classical vector ck = PRk l=1(ck)l |r (k) l ⟩, and i[H, Pj ] is calculated through projecting onto the subspace Sk and evaluating the expectation classicaly using the classical vector ck.[49]. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: QCELS results from sample data of the orbital rotated Hubbard Hamiltonian on 28 qubits [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Classical pre-processing phase - training a regressor on smaller systems. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum Eigensolver use case. We trained two small models on classically mined data from systems with up to 16 qubits, using XGBoost's Python regressor. We evaluated our preliminary approach on 20-, 24- and 28-qubit systems by optimising the Eigensolver's hyperparameters. These models predict hyperparameter values, leading to a 0.12% reduction in error when tested on 28-qubit systems. However, due to inconclusive results with 20- and 24-qubit systems, we suggest further examination of the training data based on Hamiltonian characteristics. In future work, we plan to train machine learning models to optimise other aspects or subroutines of quantum algorithm execution beyond its hyperparameters.

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

3 major / 0 minor

Summary. The manuscript proposes accelerating Quantum Eigensolver algorithms on NISQ devices by training XGBoost regressors on classically mined data from systems of up to 16 qubits to predict hyperparameters for 20-, 24-, and 28-qubit instances. It reports that these models yield a 0.12% error reduction on 28-qubit systems while noting inconclusive outcomes for the 20- and 24-qubit cases, and recommends re-examining the training data by Hamiltonian characteristics.

Significance. If the reported generalization and error reduction were shown to be robust and statistically meaningful across a broader set of Hamiltonians, the approach could offer a practical route to hyperparameter optimization for variational quantum algorithms. However, the 0.12% gain is modest, the results are mixed across system sizes, and no details on training, validation, or baselines are supplied, so the potential impact remains speculative at present.

major comments (3)
  1. [Abstract] Abstract: The central claim that ML-predicted hyperparameters accelerate the eigensolver rests on transfer from ≤16-qubit training data to 20–28-qubit test systems, yet the abstract supplies no information on the Hamiltonians, feature vectors, training/validation splits, or any baseline comparison, rendering the generalization assumption unverifiable.
  2. [Abstract] Abstract: The reported 0.12% error reduction on 28 qubits is presented without error bars, statistical tests, or comparison to standard hyperparameter search methods; given that the outcomes are explicitly inconclusive for the 20- and 24-qubit cases, this gain does not yet establish a reliable acceleration.
  3. [Abstract] Abstract: The authors themselves note that further examination of training data by Hamiltonian characteristics is needed, which indicates that the current empirical setup does not support the claimed transferability and therefore weakens the load-bearing premise of the work.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive comments on our preliminary study. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that ML-predicted hyperparameters accelerate the eigensolver rests on transfer from ≤16-qubit training data to 20–28-qubit test systems, yet the abstract supplies no information on the Hamiltonians, feature vectors, training/validation splits, or any baseline comparison, rendering the generalization assumption unverifiable.

    Authors: The abstract is a concise summary and omits these specifics due to length constraints. We will revise the abstract to note that training used classically computed data from molecular Hamiltonians on systems of up to 16 qubits, with features based on system size and Hamiltonian properties, and that ML predictions were compared to the eigensolver's default hyperparameters. revision: yes

  2. Referee: [Abstract] Abstract: The reported 0.12% error reduction on 28 qubits is presented without error bars, statistical tests, or comparison to standard hyperparameter search methods; given that the outcomes are explicitly inconclusive for the 20- and 24-qubit cases, this gain does not yet establish a reliable acceleration.

    Authors: We agree the reported gain is modest and the abstract lacks error bars or statistical tests. This is an exploratory result from a small-scale study. We will revise the abstract to explicitly state that the 0.12% improvement on 28 qubits is small, results for 20- and 24-qubit systems were inconclusive, and no exhaustive search baselines were feasible for the larger instances. revision: yes

  3. Referee: [Abstract] Abstract: The authors themselves note that further examination of training data by Hamiltonian characteristics is needed, which indicates that the current empirical setup does not support the claimed transferability and therefore weakens the load-bearing premise of the work.

    Authors: The note on further examination reflects the mixed results across sizes and is presented transparently as a limitation rather than a claim of broad transferability. The work's premise is that ML offers a preliminary route to modest acceleration in select cases (as seen for 28 qubits), with the suggestion for Hamiltonian-specific analysis intended to inform future refinements, not to indicate the setup is unsupported. revision: no

standing simulated objections not resolved
  • Exact details on feature vectors, training/validation splits, and baseline methods, which are not described in the provided abstract.

Circularity Check

0 steps flagged

No circularity: empirical ML training on independent classical data

full rationale

The paper reports training XGBoost regressors on classically mined data from systems ≤16 qubits and evaluating hyperparameter predictions on 20-28 qubit instances, yielding a small observed error reduction on the largest case. No derivation chain, equations, self-citations, or ansatzes are present in the available abstract. The approach is a standard supervised learning pipeline with no reduction of outputs to inputs by construction or load-bearing self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that small-system data generalizes to larger qubit counts.

axioms (1)
  • domain assumption Data mined from smaller qubit systems is representative for training models that generalize to larger systems
    This premise is required for the evaluation on 20-28 qubit systems to be meaningful.

pith-pipeline@v0.9.0 · 5665 in / 1062 out tokens · 43695 ms · 2026-05-23T20:09:26.967222+00:00 · methodology

discussion (0)

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Reference graph

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