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arxiv: 2305.19014 · v1 · submitted 2023-05-30 · 🪐 quant-ph

Implementing Jastrow--Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm

John P. T. Stenger , C. Stephen Hellberg , Daniel Gunlycke This is my paper

Pith reviewed 2026-05-24 08:27 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Jastrow-Gutzwiller operatorcascaded variational quantum eigensolverHubbard modelnon-unitary operatorsquantum computingmany-body correlations
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The pith

The cascaded variational quantum eigensolver implements the non-unitary Jastrow-Gutzwiller operator on quantum hardware for the Hubbard model.

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

The paper demonstrates a method to apply a Jastrow-Gutzwiller operator, which introduces many-body correlations to a quantum state but cannot be directly executed because it is non-unitary. The approach uses the cascaded variational quantum eigensolver algorithm to achieve the operator's effects through a sequence of variational steps on quantum devices. The technique is shown on IBM Q Lagos for the Hubbard model, allowing variational calculations to incorporate strong electron correlations. A sympathetic reader would care because this removes a barrier to using established many-body wavefunction forms in near-term quantum computing.

Core claim

The cascaded variational quantum eigensolver algorithm provides a practical route to realizing the effects of the non-unitary Jastrow-Gutzwiller operator on quantum hardware, as demonstrated through its application to the Hubbard model on IBM Q Lagos.

What carries the argument

The cascaded variational quantum eigensolver algorithm, which approximates the action of the non-unitary Jastrow-Gutzwiller operator through successive variational optimizations.

If this is right

  • Variational quantum calculations for the Hubbard model can now include explicit Jastrow-Gutzwiller correlations without requiring a unitary reformulation.
  • The same cascaded procedure extends to other non-unitary many-body operators that add correlations beyond mean-field states.
  • Ground-state approximations on quantum hardware become feasible for models where the Jastrow-Gutzwiller factor improves accuracy over simpler ansatzes.

Where Pith is reading between the lines

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

  • The method could be tested on larger Hubbard lattices to check whether hardware noise limits the depth of the cascaded circuit.
  • Similar cascaded implementations might apply to other correlation factors used in quantum chemistry, such as those appearing in coupled-cluster theory.
  • If the approach scales, it would allow direct benchmarking of Jastrow-Gutzwiller states against other variational methods on the same quantum device.

Load-bearing premise

The cascaded variational quantum eigensolver algorithm can reproduce the effects of the non-unitary Jastrow-Gutzwiller operator on quantum hardware.

What would settle it

Running the cascaded algorithm on the Hubbard model and finding ground-state energies or correlation functions that differ substantially from those obtained by classical application of the Jastrow-Gutzwiller operator to the same initial state.

Figures

Figures reproduced from arXiv: 2305.19014 by C. Stephen Hellberg, Daniel Gunlycke, John P. T. Stenger.

Figure 1
Figure 1. Figure 1: FIG. 1. Lattices used to demonstrate the algorithm: (a) A [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Ground-state energy for the square and triangular [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Circuit model specifications. a) layout of the IBM Lagos device. Qubits are depicted as circles and the connectivity [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

A Jastrow--Gutzwiller operator adds many-body correlations to a quantum state. However, the operator is non-unitary, making it difficult to implement directly on a quantum computer. We present a novel implementation of the Jastrow--Gutzwiller operator using the cascaded variational quantum eigensolver algorithm. We demonstrate the method on IBM Q Lagos for a Hubbard model.

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 / 0 minor

Summary. The manuscript claims to present a novel implementation of the non-unitary Jastrow-Gutzwiller operator on quantum hardware via the cascaded variational quantum eigensolver (CVQE) algorithm, with a demonstration on IBM Q Lagos for the Hubbard model.

Significance. If the central claim holds with supporting derivations, benchmarks, and error analysis, the work would address a practical obstacle in variational quantum algorithms by enabling non-unitary correlation factors on NISQ devices, which could improve accuracy for strongly correlated fermionic systems.

major comments (1)
  1. [Abstract] Abstract: the central claim that CVQE implements the effects of the non-unitary Jastrow-Gutzwiller operator is stated without any equations, circuit construction, measurement protocol, or quantitative results, so the soundness of the method cannot be assessed from the provided text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. We address the single major comment below regarding the abstract.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that CVQE implements the effects of the non-unitary Jastrow-Gutzwiller operator is stated without any equations, circuit construction, measurement protocol, or quantitative results, so the soundness of the method cannot be assessed from the provided text.

    Authors: Abstracts are by design concise summaries and do not contain the technical details requested. The full manuscript provides the explicit equations for the cascaded VQE implementation of the Jastrow-Gutzwiller operator, the corresponding quantum circuit constructions, the measurement protocol, and quantitative benchmark results on IBM Q Lagos for the Hubbard model. The soundness of the method is therefore assessable from the complete text rather than the abstract alone. revision: no

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract and provided context contain no derivations, equations, parameter definitions, or self-citations that could be walked for circular reduction. The central claim of a novel implementation via cascaded VQE is stated without visible steps that equate to inputs by construction, fitted predictions renamed as results, or load-bearing self-citations. Per the rules, an honest non-finding applies when no quotable evidence of circularity exists; the paper's content as given is self-contained against external benchmarks for this analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are described in the abstract.

pith-pipeline@v0.9.0 · 5597 in / 1106 out tokens · 32289 ms · 2026-05-24T08:27:36.395757+00:00 · methodology

discussion (0)

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Reference graph

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