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arxiv: 2504.04021 · v2 · submitted 2025-04-05 · 🪐 quant-ph

Direct entanglement ansatz learning (DEAL) with ZNE on error-prone superconducting qubits

Ziqing Guo , Steven Rayan , Wenshuo Hu , Ziwen Pan This is my paper

Pith reviewed 2026-05-22 21:41 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum optimizationQAOAentanglement ansatzzero noise extrapolationsuperconducting qubitscombinatorial optimizationerror mitigationQUBO
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The pith

Direct mapping from problem parameters to quantum ansatz angles with zero-noise extrapolation improves optimization success on noisy superconducting qubits.

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

The paper presents Direct Entanglement Ansatz Learning as a method that directly translates the coefficients of a quadratic unconstrained binary optimization problem into the rotation angles of a quantum circuit's cost and mixer Hamiltonians. This mapping is used within an entanglement-based ansatz to navigate the solution space more effectively than standard approaches. Zero-noise extrapolation is applied to suppress the impact of hardware noise such as crosstalk and coherence loss. Experiments on superconducting qubits show that this combination raises the success rate by as much as 14 percent over the quantum approximate optimization algorithm and maintains lower error variance. The approach is tested on traveling salesman, knapsack, and max-cut instances where it reaches near-optimal ground-state energies.

Core claim

DEAL uses a direct mapping from quadratic unconstrained binary problem parameters to the angles of the cost and mixer Hamiltonians in an entanglement ansatz, paired with zero noise extrapolation, to improve convergence and deliver higher success rates and near-optimum solutions for combinatorial optimization problems on error-prone superconducting qubits.

What carries the argument

Direct Entanglement Ansatz Learning (DEAL), a technique that performs a direct mapping from quadratic unconstrained binary optimization parameters to quantum ansatz angles for the cost and mixer Hamiltonians.

If this is right

  • DEAL achieves success rates up to 14 percent higher than the quantum approximate optimization algorithm on the tested problems.
  • Error variance is controlled more effectively than in the baseline method.
  • Near-optimum ground energy solutions are obtained for traveling salesman, knapsack, and max-cut problems.
  • The method extends the practical use of quantum optimization to current noisy intermediate-scale quantum hardware.

Where Pith is reading between the lines

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

  • If the direct mapping reduces the optimization landscape complexity, it may lower the classical computational overhead in hybrid quantum-classical solvers.
  • Success on multiple NP-hard problem classes suggests the technique could apply to other combinatorial tasks without major reformulation.
  • Hardware-specific tuning of the zero-noise extrapolation scale factors might further boost performance on different qubit platforms.

Load-bearing premise

The direct mapping from quadratic unconstrained binary problem parameters to ansatz angles improves convergence without adding bias or optimization difficulties, and zero-noise extrapolation sufficiently mitigates the dominant errors on the superconducting hardware.

What would settle it

A side-by-side run of DEAL and standard QAOA on the same superconducting device for identical problem instances that shows no increase in success rate or higher error variance would falsify the main experimental claim.

Figures

Figures reproduced from arXiv: 2504.04021 by Steven Rayan, Wenshuo Hu, Ziqing Guo, Ziwen Pan.

Figure 1
Figure 1. Figure 1: The proof-of-concept workflow for DEAL. involves the QPN utilizing objective weights from the QUBO to the XY mixer Hamiltonian, followed by mapping to the real QPU topology. The variable γ represents the single rotation angles, whereas β denotes the controlled rotation angles, which range from 0 to π. Additionally, the adaptive ZNE with Pauli gate insertion between the quantum ansatz and the rotation is re… view at source ↗
Figure 2
Figure 2. Figure 2: Top: Solid lines represent observable values for Rz rotation cost Hamiltonian with X and Y bases. Bottom: XY mixer Hamiltonian observables are encoded using sin function (solid lines). Dashed lines indicate encoding methods not employed in our experiment. over qubits, yielding initial parameters shown in Eq. (10) γ 0 k = 1 n X i Φ γ k,i, β0 k = 1 n X i Φ β k,i. (10) Fixed initialization provides zero varia… view at source ↗
Figure 4
Figure 4. Figure 4: The figure shows the detail of convergence [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: (Left) cumulative distribution functions (CDFs) of measurement outcome probabilities for DEAL and QAOA algorithms across 500 independent runs on a 4- qubit complete graph (graph refer in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The number of qubits requirement as the increas [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance comparison of vanilla QAOA and DEAL algorithms executed on IBM 133-qubit Torino (above) and 156-qubit Marrakesh (below). The shaded area indicates the error rate. We note that the standard deviation gradually decreases as the quantum circuit simulation evolves, indicating improved optimization convergence before implementing the seven layers. However, superconducting qubit deco￾herence limitati… view at source ↗
Figure 7
Figure 7. Figure 7: Numerical simulation conducted on ideal statevector simulator with default 1,024 shots utilizing [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The top panel shows the encoded cost and mixer [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Quantum state probability distribution comparison between DEAL (top) and QAOA (bottom) algorithms across [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
read the original abstract

Quantum combinatorial optimization algorithms typically face challenges due to complex optimization landscapes featuring numerous local minima, exponentially scaling latent spaces, and susceptibility to quantum hardware noise. In this study, we introduce Direct Entanglement Ansatz Learning (DEAL), wherein we employ a direct mapping from quadratic unconstrained binary problem parameters to quantum ansatz angles for cost and mixer hamiltonians, which improves the convergence rate towards the optimal solution. Our approach exploits a quantum entanglement-based ansatz to effectively explore intricate latent spaces and zero noise extrapolation (ZNE) to greatly mitigate the randomness caused by crosstalk and coherence errors. Our experimental evaluation demonstrates that DEAL increases the success rate by up to 14% compared to the classic quantum approximation optimization algorithm while also controlling the error variance. In addition, we demonstrate the capability of DEAL to provide near optimum ground energy solutions for travelling salesman, knapsack, and maxcut problems, which facilitates novel paradigms for solving relevant NP-hard problems and extends the practical applicability of quantum optimization using noisy 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 manuscript introduces Direct Entanglement Ansatz Learning (DEAL), a direct mapping from QUBO problem parameters to quantum ansatz angles for cost and mixer Hamiltonians within an entanglement-based ansatz. Combined with zero-noise extrapolation (ZNE), the approach is claimed to improve convergence rates and mitigate crosstalk/coherence errors on superconducting qubits. Experimental results report up to 14% higher success rates than standard QAOA, controlled error variance, and near-optimal ground-state energies for traveling salesman, knapsack, and max-cut instances.

Significance. If the empirical claims hold, DEAL could extend the practical reach of variational quantum optimization on NISQ hardware by reducing optimization difficulties through a direct parameter mapping and applying ZNE for noise control. The multi-problem demonstration is a positive aspect, though the purely experimental nature (no machine-checked proofs or parameter-free derivations) limits theoretical novelty.

major comments (2)
  1. [Abstract and experimental evaluation] The central experimental claim (14% success-rate lift and variance control) rests on the assertion that the direct QUBO-to-angle mapping plus ZNE suffices to mitigate coherence and crosstalk errors. Standard ZNE extrapolates under a global noise-strength parameter, yet crosstalk on fixed-frequency transmons is spatially correlated and does not necessarily obey the same scaling; if the implementation only varies a single global factor without isolating crosstalk (e.g., via spectator-qubit or frequency-detuning sweeps), the reported variance reduction could be instance- or post-selection-dependent rather than general. This assumption is load-bearing for the noise-mitigation conclusion.
  2. [Methods and results] The direct mapping from QUBO parameters to ansatz angles is presented as improving convergence without introducing new optimization difficulties or bias, but no explicit check (e.g., comparison of optimization landscapes or bias metrics across problem sizes) is described to confirm this. This is load-bearing for the claim that DEAL avoids the usual QAOA pitfalls.
minor comments (2)
  1. [Notation and ansatz definition] Provide the exact functional form of the direct mapping from QUBO coefficients to rotation angles, including any normalization or scaling factors, to enable reproducibility.
  2. [Experimental evaluation] Report the number of random seeds, circuit executions per instance, and post-selection rules used in the success-rate statistics; the current presentation leaves robustness unclear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major point below and indicate the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract and experimental evaluation] The central experimental claim (14% success-rate lift and variance control) rests on the assertion that the direct QUBO-to-angle mapping plus ZNE suffices to mitigate coherence and crosstalk errors. Standard ZNE extrapolates under a global noise-strength parameter, yet crosstalk on fixed-frequency transmons is spatially correlated and does not necessarily obey the same scaling; if the implementation only varies a single global factor without isolating crosstalk (e.g., via spectator-qubit or frequency-detuning sweeps), the reported variance reduction could be instance- or post-selection-dependent rather than general. This assumption is load-bearing for the noise-mitigation conclusion.

    Authors: We acknowledge that standard ZNE relies on a global noise model and that crosstalk on fixed-frequency transmons is spatially correlated, which may not scale identically. In the experiments, ZNE was applied via global noise scaling (pulse stretching), and the observed variance reduction in success rates was consistent across the TSP, knapsack, and max-cut instances. While dedicated isolation experiments (e.g., spectator-qubit sweeps) were not performed, the multi-instance empirical results support practical effectiveness. We have revised the manuscript to include a dedicated discussion of ZNE limitations for correlated noise and additional implementation details. revision: partial

  2. Referee: [Methods and results] The direct mapping from QUBO parameters to ansatz angles is presented as improving convergence without introducing new optimization difficulties or bias, but no explicit check (e.g., comparison of optimization landscapes or bias metrics across problem sizes) is described to confirm this. This is load-bearing for the claim that DEAL avoids the usual QAOA pitfalls.

    Authors: The direct QUBO-to-angle mapping is designed to provide a problem-informed starting point that reduces the burden on variational optimization. The reported higher success rates and near-optimal energies across problem sizes provide empirical evidence against significant introduced bias. We agree that explicit landscape or bias-metric comparisons would strengthen the claim and have added such an analysis (including optimization trajectory comparisons) to the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental claims are self-contained

full rationale

The paper reports empirical success-rate improvements (up to 14%) and near-optimum solutions for TSP/knapsack/maxcut as direct hardware outcomes of DEAL plus ZNE. No equations, fitted parameters renamed as predictions, or self-citation chains appear in the abstract or described claims that would reduce the central result to its own inputs by construction. The direct QUBO-to-angle mapping and ZNE usage are presented as methodological choices whose performance is measured externally on superconducting hardware, not derived from the measured quantities themselves. This is the normal non-circular case for an experimental methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only view supplies no explicit free parameters, axioms, or invented entities beyond the named method itself.

invented entities (1)
  • Direct Entanglement Ansatz Learning (DEAL) no independent evidence
    purpose: Direct mapping from QUBO parameters to ansatz angles
    New named procedure introduced to improve convergence.

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discussion (0)

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    8: The top panel shows the encoded cost and mixer Hamiltonian values

    XY mixer Hamiltonian parameters for RXX +Y Y (βKij) gates receive normalized Fig. 8: The top panel shows the encoded cost and mixer Hamiltonian values. The bottom panel demonstrates the nonlinear PQN scaling plot corresponding to Eq. (7) and Eq. (8). coupling strengths: K01 = |α| |α| + |β| + |γ| + |δ| , (18) K02 = |β| |α| + |β| + |γ| + |δ| , (19) K12 = |γ...

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  56. [56]

    The initialization follows {Jij, Kij} → { Φγ k,i, Φβ k,i} → { γ0 k, β0 k}, creating direct mapping from problem structure to quantum circuit parameters

    Quantum state amplitudes reference the (p × n) tensors Φγ k,i and Φβ k,i encoding layer-dependent (k) and qubit-dependent ( i) information from graph weights {α, β, γ, δ}. The initialization follows {Jij, Kij} → { Φγ k,i, Φβ k,i} → { γ0 k, β0 k}, creating direct mapping from problem structure to quantum circuit parameters. We conclude that the computation...

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