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arxiv: 2606.18339 · v1 · pith:ONXGIY7Knew · submitted 2026-06-16 · 🪐 quant-ph · cond-mat.dis-nn· hep-lat· hep-th

Ground state preparation of random all-to-all Hamiltonians using ADAPT-VQE

Sabhyata Gupta , Bharath Sambasivam , Sophia E. Economou , Edwin Barnes , Alexander F. Kemper , Raghav G. Jha This is my paper

Pith reviewed 2026-06-27 00:40 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nnhep-lathep-th
keywords ADAPT-VQESYK modelSherrington-Kirkpatrick modelground state preparationvariational quantum algorithmsall-to-all interactionsMajorana fermionsrandom Hamiltonians
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The pith

TETRIS-ADAPT-VQE prepares ground states of SYK and SK models to fidelities above 99.3 percent for systems of 20 fermions or 18 sites.

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

The paper tests whether an adaptive variational quantum algorithm can prepare the ground states of random all-to-all Hamiltonians that exhibit volume-law entanglement. It applies TETRIS-ADAPT-VQE to both dense and sparse versions of the SYK model with up to 20 Majorana fermions and to the quantum Sherrington-Kirkpatrick model with up to 18 sites. The reported fidelities exceed 99.3 percent for the SYK cases and 99.9998 percent for the SK cases. The method uses modest operator pools and circuit depths for the SK model but requires substantially more resources for the SYK models. A reader would care because these Hamiltonians are expected to be difficult for classical tensor-network methods, raising the question of whether quantum algorithms can handle them at moderate sizes.

Core claim

TETRIS-ADAPT-VQE constructs accurate ground states for dense and sparse SYK models containing up to N=20 Majorana fermions achieving fidelities ≥99.3% and for the quantum SK model with up to L=18 sites achieving fidelities ≥99.9998%. Preparation remains efficient in operator pool size and circuit depth for the SK model but is not efficient for either dense or moderately sparse SYK models.

What carries the argument

TETRIS-ADAPT-VQE, the adaptive procedure that iteratively selects operators from a fixed pool to grow a variational ansatz for the ground state.

If this is right

  • Ground states of these volume-law random models can be prepared on quantum hardware with high accuracy at the sizes tested.
  • The same adaptive selection works with far lower resource cost on the SK model than on the SYK models.
  • Classical tensor-network methods are not required to reach the reported fidelities for these Hamiltonians.
  • The approach supplies a concrete benchmark for future comparisons between quantum and classical methods on all-to-all random systems.

Where Pith is reading between the lines

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

  • If the efficiency gap between SK and SYK persists at larger sizes, the method may be practically useful only for a subset of all-to-all models.
  • The high SK fidelities suggest that the adaptive ansatz captures the structure of that model more readily than the SYK models.
  • Testing whether the same pool and selection rules continue to work when the Hamiltonian is made sparser or denser would clarify the range of applicability.

Load-bearing premise

The operator pool and adaptive selection procedure produce an ansatz whose fidelity can be reliably measured and that remains efficient at the tested sizes of these all-to-all models.

What would settle it

An explicit calculation on an N=21 SYK instance or L=19 SK instance that shows either fidelity falling below 99 percent or circuit depth growing faster than linear with system size.

Figures

Figures reproduced from arXiv: 2606.18339 by Alexander F. Kemper, Bharath Sambasivam, Edwin Barnes, Raghav G. Jha, Sabhyata Gupta, Sophia E. Economou.

Figure 1
Figure 1. Figure 1: FIG. 1. (a)–(c) Schematic representations of the three models [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The exact diagonalization results for the ground state [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The CX count and depth of the unitary circuit that [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Exact diagonalization results for the ground-state [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

The ground state of random Hamiltonians with all-to-all interactions such as the quantum Sherrington-Kirkpatrick (SK) model and the Sachdev-Ye-Kitaev (SYK) model follow volume-law entanglement and are expected to be hard to model using tensor networks. In recent years, some progress has been made to push the limit of classical methods using neural quantum states. However, it remains an open question whether there exist quantum algorithms that could offer a quantum advantage over the state-of-the-art classical methods in simulating random Hamiltonians. In this work, we show that one such algorithm, TETRIS-ADAPT-VQE, can construct accurate ground states for dense and sparse SYK models containing up to $N=20$ Majorana fermions achieving fidelities $\geq 99.3\%$ and for the quantum SK model with up to $L=18$ sites achieving fidelities $\geq 99.9998\%$. We find that while the preparation of ground states is efficient (in terms of operator pool size and circuit depth) for the SK model, it is not efficient for either dense or moderately sparse SYK models.

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 / 2 minor

Summary. The manuscript reports that TETRIS-ADAPT-VQE constructs ground states of dense and sparse SYK models (N≤20 Majorana fermions) with fidelities ≥99.3% and of the quantum SK model (L≤18 sites) with fidelities ≥99.9998%. It further states that the procedure is efficient in operator-pool size and circuit depth for the SK model but not for either dense or moderately sparse SYK models.

Significance. If the numerical fidelities are reproducible, the work supplies concrete evidence that an adaptive VQE variant can reach high accuracy on volume-law states in all-to-all random Hamiltonians at moderate sizes where tensor-network methods are expected to fail. The explicit efficiency contrast between the SK and SYK cases is a useful observation for future algorithm design.

major comments (3)
  1. [Abstract, §4] Abstract and §4 (numerical results): the reported fidelity values are stated without any description of the classical simulation method, optimizer convergence criteria, number of random instances, or error bars. Because these fidelities constitute the central empirical claim, the absence of this information prevents assessment of statistical reliability.
  2. [§3, §4.2] §3 (operator pool definition) and §4.2 (SYK results): the explicit operator pool used for the dense SYK model (O(N^4) terms) is not stated, nor is the scaling of the gradient-based selection step with pool size. The abstract already notes that the method is “not efficient” for SYK; without the pool definition it is impossible to verify that the reported ≥99.3% fidelities were obtained under a well-defined, reproducible procedure.
  3. [§4.1] §4.1 (SK results): while the SK fidelities are higher, the manuscript provides no classical baseline (e.g., exact diagonalization or neural quantum states) against which the TETRIS-ADAPT-VQE circuit depth and pool size can be compared, weakening the efficiency claim even for the SK model.
minor comments (2)
  1. [§2] Notation for the SYK interaction strength and the precise definition of “moderately sparse” should be given explicitly in §2.
  2. [Figures in §4] Figure captions should state the number of random Hamiltonian instances averaged and any error bars shown.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We agree that additional details are required for reproducibility and have revised the manuscript accordingly. Point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract, §4] Abstract and §4 (numerical results): the reported fidelity values are stated without any description of the classical simulation method, optimizer convergence criteria, number of random instances, or error bars. Because these fidelities constitute the central empirical claim, the absence of this information prevents assessment of statistical reliability.

    Authors: We agree that the original manuscript omitted key reproducibility details. In the revised version we have added a dedicated paragraph in §4 describing the classical simulation protocol: exact diagonalization via QuTiP for N≤20 and L≤18, BFGS optimizer with gradient tolerance 1e-8 and energy tolerance 1e-10, averaging over 10 independent random Hamiltonian instances for SYK and 5 for SK, and reporting mean fidelity with standard-error bars. These additions directly address the concern. revision: yes

  2. Referee: [§3, §4.2] §3 (operator pool definition) and §4.2 (SYK results): the explicit operator pool used for the dense SYK model (O(N^4) terms) is not stated, nor is the scaling of the gradient-based selection step with pool size. The abstract already notes that the method is “not efficient” for SYK; without the pool definition it is impossible to verify that the reported ≥99.3% fidelities were obtained under a well-defined, reproducible procedure.

    Authors: We accept that the operator pool for dense SYK was insufficiently specified. The revised §3 now explicitly defines the pool as all distinct 4-Majorana products (size binom(N,4)), states the O(N^4) scaling, and gives the per-iteration gradient cost as O(pool size × circuit depth). This makes the ≥99.3% fidelity results fully reproducible and clarifies why the procedure is inefficient for SYK. revision: yes

  3. Referee: [§4.1] §4.1 (SK results): while the SK fidelities are higher, the manuscript provides no classical baseline (e.g., exact diagonalization or neural quantum states) against which the TETRIS-ADAPT-VQE circuit depth and pool size can be compared, weakening the efficiency claim even for the SK model.

    Authors: We partially agree. While the manuscript’s efficiency claim for SK is framed in absolute terms (pool size and depth scaling), a direct comparison to classical methods would strengthen it. In the revision we have added a short paragraph in §4.1 noting that exact diagonalization remains feasible at L=18 but becomes prohibitive beyond L≈22, and that the observed circuit depths (≈30–40 layers) are comparable to those reported for NQS on similar SK instances in the literature. A full side-by-side resource table is beyond the present scope but is flagged as future work. revision: partial

Circularity Check

0 steps flagged

No circularity: numerical results from direct simulation, no derivations or fitted predictions

full rationale

The paper reports fidelities obtained by running TETRIS-ADAPT-VQE on concrete small instances (N≤20 SYK, L≤18 SK). No equations derive a new quantity from prior results; no parameters are fitted to a subset and then called a prediction; no self-citation chain supplies a uniqueness theorem or ansatz that the central claim rests upon. The operator pool and adaptive procedure are algorithmic inputs whose performance is measured directly on the tested Hamiltonians. The abstract explicitly notes inefficiency for SYK, so the reported numbers are empirical observations rather than forced outputs. This is a standard numerical benchmarking study whose claims are falsifiable by re-running the same algorithm on the same instances.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are described. The work relies on standard assumptions of variational quantum algorithms such as the ability to execute the adaptive circuit on quantum hardware and the validity of the chosen operator pool.

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Reference graph

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