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arxiv: 2605.30572 · v1 · pith:CGBTVVJZnew · submitted 2026-05-28 · 🪐 quant-ph

Mitigating Noise-Induced Barren Plateaus Using a Non-Unitary Ansatz: Application to Molecular Electronic Transport

Sasanka Dowarah , Abeda Sultana Shamma , Yazdan Maghsoud , G. Andr\'es Cisneros , Michael Kolodrubetz This is my paper

Pith reviewed 2026-06-29 06:22 UTC · model grok-4.3

classification 🪐 quant-ph
keywords variational quantum algorithmsnoise-induced barren plateausnon-unitary ansatzopen quantum systemsmolecular electronic transportdepolarizing noisequantum chemistry
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The pith

Non-unitary elements in variational ansatze restore finite gradients under depolarizing noise for open quantum systems.

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

This paper shows that adding non-unitary operations to variational quantum circuits can prevent gradients from vanishing due to noise in simulations of open quantum systems. It tests this on an infinite-range dissipative Ising model where the non-unitary ansatz allows optimization to reach the correct steady state with broken symmetry. The approach is then applied to a first-principles model of electron transport through a molecular junction. If true, this offers a way to run useful variational algorithms on current noisy hardware for chemistry problems involving dissipation.

Core claim

The central claim is that a nonunitary ansatz restores finite gradients in the presence of depolarizing noise, enabling convergence to the correct symmetry-broken steady state in open quantum systems. Using an analytically tractable infinite-range dissipative Ising model, the nonunitary ansatz succeeds where unitary ones fail. A Floquet-type ansatz with repeated parameters reduces the circuit to an effective quantum channel for analysis. Extension to OPE-SMe molecular transport with first-principles Hamiltonians and jump operators shows the method works for realistic systems.

What carries the argument

The non-unitary variational ansatz, which incorporates non-unitary elements to mitigate noise-induced barren plateaus by maintaining finite gradients.

If this is right

  • Finite gradients allow optimization to the symmetry-broken steady state in the dissipative Ising model despite noise.
  • The Floquet-type ansatz enables direct analysis of fixed points as an effective quantum channel.
  • Non-unitary ansatze enable simulation of electron transport in OPE-SMe on NISQ hardware.
  • Provides a scalable route for open-system steady states on noisy hardware.

Where Pith is reading between the lines

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

  • The method might generalize to other open quantum chemistry problems beyond the tested models.
  • Combining non-unitary ansatze with error mitigation could further improve performance on real devices.
  • Testing on larger molecular systems would check if the gradient restoration scales.
  • Exploring different types of non-unitary operations could optimize the approach for specific noise models.

Load-bearing premise

That success on the infinite-range Ising model and the specific OPE-SMe system means the non-unitary mitigation will work for general open quantum chemistry problems.

What would settle it

If a non-unitary ansatz applied to a different open quantum system or noise model still shows exponentially vanishing gradients with depth, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.30572 by Abeda Sultana Shamma, G. Andr\'es Cisneros, Michael Kolodrubetz, Sasanka Dowarah, Yazdan Maghsoud.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Standard unitary variational ansatz with depolarizing noise interleaved between layers. As the system size or [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic of a variational quantum algorithm. An [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Steady state phase diagram with the mean-field order [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A single-layer variational quantum circuit for the mean-field model with each unitary and non-unitary gates sandwiched [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Plot of standard deviation of the gradients averaged [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Floquet variational ansatz where each layer shares [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Heatmap of the steady-state order-parameter magnitude [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Schematic of electron transport model through [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Trotterized Lindbladian time evolution of the molecu [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. a) Gas-phase OPE-SMe geometry at the B3LYP/6-31+G(d,p) level. b) Radial distribution function [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The observable [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Charge current as a function of number of it [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Zero-noise–extrapolated steady-state currents ob [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Circuit implementation of the [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Implementation of [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Example quantum circuit to implement [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
read the original abstract

Variational quantum algorithms (VQAs) offer a promising route toward simulating many-body quantum systems on noisy intermediate-scale quantum (NISQ) hardware. However, their scalability is severely limited by noise-induced barren plateaus (NIBPs), where hardware noise causes the gradients of the cost function to vanish exponentially with circuit depth, rendering optimization impossible. In this work, we demonstrate that introducing nonunitary elements into the variational ansatz can mitigate NIBPs in open-quantum systems. Using an analytically tractable infinite-range dissipative Ising model, we show that a nonunitary ansatz restores finite gradients in the presence of depolarizing noise, enabling convergence to the correct symmetry-broken steady state. We also develop a Floquet-type variational ansatz in which each layer repeats the same parameters, reducing the deep variational circuit to an effective quantum channel whose fixed points can be analyzed directly. We then extend these ideas to a realistic quantum-chemistry system by simulating electron transport through Oligophenylethynylene-sulfurmethyl (OPE-SMe) using Hamiltonians and jump operators of the model derived from first-principles polarizable QM/MM calculations. Our results show that nonunitary variational ans\"atze provide a scalable and physically grounded route for simulating open-system steady states on NISQ hardware, offering a pathway to overcoming one of the limitations of current quantum 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 / 2 minor

Summary. The paper claims that non-unitary elements in the variational ansatz mitigate noise-induced barren plateaus (NIBPs) for open quantum systems on NISQ hardware. Using an analytically tractable infinite-range dissipative Ising model with depolarizing noise, a non-unitary ansatz is shown to restore finite gradients and enable convergence to the symmetry-broken steady state. A Floquet-type ansatz with repeated parameters reduces the circuit to an effective quantum channel for fixed-point analysis. The approach is extended to first-principles simulation of electron transport through OPE-SMe using derived Hamiltonians and jump operators, with results indicating that non-unitary ansatze offer a scalable route for open-system steady states.

Significance. If the central claim holds, the work provides a concrete strategy for overcoming NIBPs in variational simulations of open quantum systems, with direct relevance to quantum chemistry applications such as molecular electronic transport. The analytic demonstration on the Ising model and the use of a parameter-sharing Floquet structure are strengths that could generalize if supported by broader evidence.

major comments (2)
  1. [Abstract and paragraph on model choice/extension to realistic system] The claim that non-unitary ansatze provide a 'scalable and physically grounded route' for general open quantum chemistry problems (Abstract) is load-bearing but rests only on the infinite-range dissipative Ising model and the specific OPE-SMe geometry/jump operators. No scaling argument, locality analysis, or counter-example is supplied to show the gradient-restoration mechanism is insensitive to interaction range or the form of the dissipators, as required for the broad applicability asserted.
  2. [Section on infinite-range dissipative Ising model] In the Ising-model section, the analytic restoration of gradients under depolarizing noise is asserted to enable convergence to the correct steady state, but the manuscript provides no explicit gradient expression or error bound showing that the non-unitary modification avoids the exponential vanishing independent of the infinite-range assumption (which may artificially suppress NIBPs).
minor comments (2)
  1. [Abstract] The abstract contains a typographical artifact ('ans"atze'); this should be corrected for clarity.
  2. [Section introducing Floquet-type variational ansatz] Notation for the Floquet-type ansatz and the effective quantum channel should be introduced with an explicit equation reference when first defined, to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped us clarify the scope and strengthen the presentation of our results. We address each major comment below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract and paragraph on model choice/extension to realistic system] The claim that non-unitary ansatze provide a 'scalable and physically grounded route' for general open quantum chemistry problems (Abstract) is load-bearing but rests only on the infinite-range dissipative Ising model and the specific OPE-SMe geometry/jump operators. No scaling argument, locality analysis, or counter-example is supplied to show the gradient-restoration mechanism is insensitive to interaction range or the form of the dissipators, as required for the broad applicability asserted.

    Authors: We agree that the original abstract phrasing overstated the generality. In the revised manuscript we have changed the abstract to state that non-unitary ansatze 'offer a promising route' for open-system steady states. We have also added a dedicated paragraph in the Discussion section that (i) explains how the Floquet parameter-sharing structure and effective-channel fixed-point analysis provide a mechanism that does not explicitly rely on infinite range, and (ii) explicitly notes the absence of a general locality or scaling proof, identifying this as an important direction for future work. revision: partial

  2. Referee: [Section on infinite-range dissipative Ising model] In the Ising-model section, the analytic restoration of gradients under depolarizing noise is asserted to enable convergence to the correct steady state, but the manuscript provides no explicit gradient expression or error bound showing that the non-unitary modification avoids the exponential vanishing independent of the infinite-range assumption (which may artificially suppress NIBPs).

    Authors: We have inserted the explicit gradient formula (new Eq. (X) in the Ising-model section) obtained from the effective quantum channel. The derivation shows that the non-unitary term prevents the gradient from decaying exponentially with depth because the variational state retains a finite overlap with the target steady state. We have added a clarifying sentence acknowledging that this expression is derived under the infinite-range assumption and that a general bound independent of interaction range lies beyond the present scope. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper introduces a non-unitary ansatz and a Floquet-type variational form, then demonstrates finite gradients and convergence on an analytically tractable infinite-range dissipative Ising model under depolarizing noise and on first-principles jump operators for the OPE-SMe system. No quoted equations reduce a claimed prediction to a fitted parameter by construction, no load-bearing uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior author work. The reported mitigation is shown via direct simulation on the chosen models rather than being forced by the input definitions or parameter choices.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that the chosen model systems capture the relevant noise and dissipation physics.

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discussion (0)

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