Expressibility, Noise, and Error Mitigation in VQE Ansatz Selection

• URL: http://arxiv.org/abs/2606.04955v1
• Date: Wed, 03 Jun 2026 14:43:24 GMT
• Title: Expressibility, Noise, and Error Mitigation in VQE Ansatz Selection
• Abstract summary: Expressibility, a metric quantifying a circuit's ability to explore the Hilbert space, has been proposed as a guide for ansatz selection.<n>We extend this investigation to cover both $H$ and $H_3+$ under four execution scenarios: ideal, noisy, and noisy with zero-noise extrapolation (ZNE) or error cancellation (PEC)<n>ZNE reduces error for only 4 of 12 $H$ circuits and 4 of 6 $H_3+$ circuits, while PEC actually increases error in 11 of 12 $H$ circuits and all 6 $H_3+$
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The variational quantum eigensolver (VQE) is a promising algorithm for near-term quantum chemistry applications, but selecting optimal ansatz circuits remains challenging. Expressibility, a metric quantifying a circuit's ability to explore the Hilbert space, has been proposed as a guide for ansatz selection, but recent work showed it inconsistently predicts VQE performance under realistic noise for $H_2$. We extend this investigation to cover both $H_2$ and $H_3^+$ under four execution scenarios: ideal, noisy, and noisy with zero-noise extrapolation (ZNE) or probabilistic error cancellation (PEC). We find that error mitigation does not reliably restore expressibility's predictive power. ZNE reduces error for only 4 of 12 $H_2$ circuits and 4 of 6 $H_3^+$ circuits, while PEC actually increases error in 11 of 12 $H_2$ circuits and all 6 $H_3^+$ circuits. We reproduce and extend Saib et al.'s key finding that circuit rankings scramble under noise (Spearman $ρ\approx -0.1$ between ideal and noisy rankings), and identify a new result: ZNE largely preserves noisy rankings ($ρ= +0.80$ for $H_2$) while PEC actively reorders them ($ρ= -0.22$). Noisy expressibility, computed from density matrix simulations, strongly predicts unmitigated performance for $H_3^+$ (Pearson $r = +0.91$, $p = 0.01$), but this metric is computationally intractable at scale. We demonstrate that zero-cost circuit topology metrics such as two-qubit gate count provide comparable or superior predictive power for PEC degradation ($r = +0.96$ for $H_3^+$), while standard expressibility best predicts noisy and ZNE performance for $H_2$ ($r = +0.74$ and $r = +0.77$).

Related papers

• Quantum amplitude estimation beyond power-of-two schedules [0.0]
  Non-adaptive quantum amplitude estimation (QAE) fixes its Grover depths in advance, so every circuit can run in parallel.<n>We show that most of this gap comes from two conventional choices: subspace-based post-processing and power-of-two depth ladders.<n>We replace the first by the exact maximum-likelihood estimate, one matrix multiplication per batch of estimates, and the second by a geometric ladder with ratio $r approx 1.45$.
  arXiv  Detail & Related papers  (2026-09-02T15:20:50Z)
• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Quantum PDE Solvers in Practice: Application-Driven Benchmarking of the Heat Equation [0.16999370482438728]
  We present a reproducible, application-driven benchmark for the 1-D Dirichlet heat equation.<n>The benchmark covers coherent linear solvers (HHL,VT, and QLS-Fourier), VQLS, imaginary-time methods (QITE, var-QITE, and AVQDS), real-time Hamiltonian simulation and unitary dilations.
  arXiv  Detail & Related papers  (2026-07-14T12:15:27Z)
• Decoherence as Defence and the Magnitude of Noise Regularisation: A Rigorous N -Qubit Theory of Stochastic Quantum Neural Networks for Adversarially Robust Network Intrusion Detection [0.0]
  We give an $N$-qubit formulation through the master equation and its vectorised Liouvillian.<n>We prove a emphdecoherence-contraction theorem: a depolarising channel of strength.<n>We show this robustness arises from a noise-reshaped training boundary rather than from attack-time contraction.
  arXiv  Detail & Related papers  (2026-06-23T07:06:56Z)
• Quantum Reservoir Autoencoder for Blind Decryption: Two-Phase Protocol and Noise Resilience [0.0]
  We instantiate the quantum reservoir autoencoder (QRA) with a noise-induced reservoir employing reset noise channels.<n>For a single-ciphertext protocol with 10 data qubits and random (non-optimized) reset probabilities, the open-system reservoir suppresses shot-noise sensitivity by ten orders of magnitude.
  arXiv  Detail & Related papers  (2026-03-12T07:05:46Z)
• Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness [74.18546828528298]
  We show that SignSGD with Majority Voting can robustly work on the whole range of complexity with $kappakappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappakappakappa-1right, kappa
  arXiv  Detail & Related papers  (2025-02-11T19:54:11Z)
• Provable Scaling Laws for the Test-Time Compute of Large Language Models [84.00141420901038]
  We propose two algorithms that enjoy provable scaling laws for the test-time compute of large language models.<n>One is a two-stage knockout-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents.<n>The other is a two-stage league-style algorithm, where each candidate is evaluated by its average win rate against multiple opponents.
  arXiv  Detail & Related papers  (2024-11-29T05:29:47Z)
• Robust Sparse Regression with Non-Isotropic Designs [4.964650614497048]
  We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries. We provide a novel analysis of weighted penalized Huber loss that is suitable for heavy-tailed designs in the presence of two adversaries.
  arXiv  Detail & Related papers  (2024-10-31T13:51:59Z)
• Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path [80.60592344361073]
  We study the Shortest Path (SSP) problem with a linear mixture transition kernel. An agent repeatedly interacts with a environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the iteration cost function or an upper bound of the expected length for the optimal policy.
  arXiv  Detail & Related papers  (2024-02-14T07:52:00Z)
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
  We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
  arXiv  Detail & Related papers  (2022-12-03T02:45:23Z)
• Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent [0.0]
  We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. For Haar random circuits with $m$ gates, we show $mathsfcoC_=P$ hardness of average-case additive approximations to an imprecision of $2-O(m)$. For random $p=1$ QAOA and IQP circuits, we show that in the average-case, it is $mathsfcoC_=P$ hard to approximate the output probability to within an additive error of $2-O(n)$
  arXiv  Detail & Related papers  (2022-06-12T02:35:51Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Provably Breaking the Quadratic Error Compounding Barrier in Imitation Learning, Optimally [58.463668865380946]
  We study the statistical limits of Imitation Learning in episodic Markov Decision Processes (MDPs) with a state space $mathcalS$. We establish an upper bound $O(|mathcalS|H3/2/N)$ for the suboptimality using the Mimic-MD algorithm in Rajaraman et al ( 2020) We show the minimax suboptimality grows as $Omega( H3/2/N)$ when $mathcalS|geq 3$ while the unknown-transition setting suffers from a larger sharp rate
  arXiv  Detail & Related papers  (2021-02-25T15:50:19Z)
• Exponential Error Suppression for Near-Term Quantum Devices [0.0]
  In NISQ era, complexity and scale required to adopt even the smallest QEC is prohibitive. We show that for the crucial case of estimating expectation values of observables one can indeed achieve an effective exponential suppression.
  arXiv  Detail & Related papers  (2020-11-11T18:00:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.