Delta-Corrected Shot Reduction for Bypassing Optimization Plateaus in Variational Quantum Eigensolvers
Abstract
The variational quantum eigensolver (VQE) remains a cornerstone hybrid quantum-classical algorithm for quantum simulation, yet its scalability is fundamentally constrained by heavy measurement overheads. While strategies such as variance-preserved shot reduction (VPSR) mitigates this cost, they suffer from convergence instability and optimization stagnation caused by finite-sample bias in limited pilot shots. To overcome this limitation, we introduce delta-corrected shot reduction (DCSR), an analytically enhanced shot allocation strategy that rigorously mitigates finite-sample instability. Utilizing the multivariate delta method, we derive explicit higher-order bias correction terms for the empirical reduction factor. Both theoretical analysis and numerical simulations reveal that incorporating higher-order statistical moments, such as skewness and kurtosis, provides the gradient resolution necessary to bypass noise-induced barren plateaus. DSCR significantly accelerates convergence compared to standard VPSR across diverse noise and resource regimes while matching or decreasing cumulative measurement costs, establishing a mathematically rigorous framework for variance-stabilized shot allocation on near-term hardware.
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BibTeX
@misc{ghozaly2026deltacorrected,
title = {{Delta-Corrected Shot Reduction for Bypassing Optimization Plateaus in Variational Quantum Eigensolvers}},
author = {Jamie Evander Ghozaly and Pekik Nurwantoro and Gagus Ketut Sunnardianto and Yanoar P. Sarwono and Leong-Chuan Kwek},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10524},
eprint = {2611.10524},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10524},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Delta-Corrected Shot Reduction for Bypassing Optimization Plateaus in Variational Quantum Eigensolvers
AU - Jamie Evander Ghozaly
AU - Pekik Nurwantoro
AU - Gagus Ketut Sunnardianto
AU - Yanoar P. Sarwono
AU - Leong-Chuan Kwek
PY - 2026
DA - 2026/11/07
PB - arXiv
DO - 10.48550/arxiv.2611.10524
UR - https://arxiv.org/abs/2611.10524
AB - The variational quantum eigensolver (VQE) remains a cornerstone hybrid quantum-classical algorithm for quantum simulation, yet its scalability is fundamentally constrained by heavy measurement overheads. While strategies such as variance-preserved shot reduction (VPSR) mitigates this cost, they suffer from convergence instability and optimization stagnation caused by finite-sample bias in limited pilot shots. To overcome this limitation, we introduce delta-corrected shot reduction (DCSR), an analytically enhanced shot allocation strategy that rigorously mitigates finite-sample instability. Utilizing the multivariate delta method, we derive explicit higher-order bias correction terms for the empirical reduction factor. Both theoretical analysis and numerical simulations reveal that incorporating higher-order statistical moments, such as skewness and kurtosis, provides the gradient resolution necessary to bypass noise-induced barren plateaus. DSCR significantly accelerates convergence compared to standard VPSR across diverse noise and resource regimes while matching or decreasing cumulative measurement costs, establishing a mathematically rigorous framework for variance-stabilized shot allocation on near-term hardware.
ER -