An iterative Bayesian variational quantum eigensolver with the von Mises-Fisher distribution
Abstract
We develop an iterative Bayesian variational quantum eigensolver in which the unknown ground state, parametrised as a real unit vector, is inferred through a von Mises--Fisher distribution sequentially updated from Hadamard-test measurements on a single ancilla qubit. Building on a companion paper that treated a single success outcome via exact moment matching, we generalise the scheme to condition on m success outcomes for the likelihood function per iteration. Since exact moment matching becomes impractical for m>1, we exploit the large-concentration regime, in which a first-order expansion of the log-likelihood yields a closed-form von Mises--Fisher posterior with m entering only through a multiplicative weight. We prove that the two convergence properties of the single-outcome scheme---non-decreasing overlap and non-decreasing concentration---are preserved provided m lies within an explicitly characterised range. Based on the theory, we propose a measurement-based algorithm and illustrate the convergence on randomly generated three- and four-qubit Hamiltonian matrices, on HeH+, and on H2.
Related
- Probability distribution analysis of the cascaded variational quantum eigensolver
- Trainable, self-verifying variational quantum eigensolver using adiabatic warm starts
- Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits
- Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits
- Mitigating Errors in Variational Quantum Eigensolver Calculations through Extended Random Phase Approximation
BibTeX
@misc{huynh2026iterative,
title = {{An iterative Bayesian variational quantum eigensolver with the von Mises-Fisher distribution}},
author = {Trung Minh Huynh and Gwangil An and Minsu Kim and Yu-Seong Jeon and Jinhyoung Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11466},
eprint = {2610.11466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11466},
}
RIS
TY - UNPB
TI - An iterative Bayesian variational quantum eigensolver with the von Mises-Fisher distribution
AU - Trung Minh Huynh
AU - Gwangil An
AU - Minsu Kim
AU - Yu-Seong Jeon
AU - Jinhyoung Lee
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11466
UR - https://arxiv.org/abs/2610.11466
AB - We develop an iterative Bayesian variational quantum eigensolver in which the unknown ground state, parametrised as a real unit vector, is inferred through a von Mises--Fisher distribution sequentially updated from Hadamard-test measurements on a single ancilla qubit. Building on a companion paper that treated a single success outcome via exact moment matching, we generalise the scheme to condition on m success outcomes for the likelihood function per iteration. Since exact moment matching becomes impractical for m>1, we exploit the large-concentration regime, in which a first-order expansion of the log-likelihood yields a closed-form von Mises--Fisher posterior with m entering only through a multiplicative weight. We prove that the two convergence properties of the single-outcome scheme---non-decreasing overlap and non-decreasing concentration---are preserved provided m lies within an explicitly characterised range. Based on the theory, we propose a measurement-based algorithm and illustrate the convergence on randomly generated three- and four-qubit Hamiltonian matrices, on HeH^+, and on H_2.
ER -