Barycentric programming: Classical realization of programs for universal quantum processors
Abstract
A programmable quantum processor implements a target unitary using information stored in a classical or quantum program register. For arbitrary unitaries in SU(d), quantum programs attain the optimal leading-order memory cost, whereas deterministic classical rounding requires twice as much memory for the same diamond-distance error. We show that this gap disappears when classical randomization is allowed. We introduce barycentric programming, which stores the label of a unitary randomly selected from a finite set, with probabilities chosen so that first-order approximation errors cancel in the averaged unitary channel. Consequently, the diamond-distance error scales quadratically with the discretization spacing. For any ν-parameter family of unitaries forming a compact, smooth manifold without boundary, this method achieves error ε using only (ν/2)log2(1/ε)+O(1) classical bits. We also prove a matching lower bound for arbitrary quantum programs, determining the optimal leading-order program size for general unitary families. Thus, classical randomization achieves the optimal scaling (ν/2+o(1))log2(1/ε) without requiring coherent quantum memory.
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BibTeX
@misc{hashimoto2026barycentric,
title = {{Barycentric programming: Classical realization of programs for universal quantum processors}},
author = {Yutaka Hashimoto and Satoshi Yoshida and Mio Murao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02441},
eprint = {2611.02441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02441},
}
RIS
TY - UNPB
TI - Barycentric programming: Classical realization of programs for universal quantum processors
AU - Yutaka Hashimoto
AU - Satoshi Yoshida
AU - Mio Murao
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02441
UR - https://arxiv.org/abs/2611.02441
AB - A programmable quantum processor implements a target unitary using information stored in a classical or quantum program register. For arbitrary unitaries in SU(d), quantum programs attain the optimal leading-order memory cost, whereas deterministic classical rounding requires twice as much memory for the same diamond-distance error. We show that this gap disappears when classical randomization is allowed. We introduce barycentric programming, which stores the label of a unitary randomly selected from a finite set, with probabilities chosen so that first-order approximation errors cancel in the averaged unitary channel. Consequently, the diamond-distance error scales quadratically with the discretization spacing. For any ν-parameter family of unitaries forming a compact, smooth manifold without boundary, this method achieves error ε using only (ν/2)log_2(1/ε)+O(1) classical bits. We also prove a matching lower bound for arbitrary quantum programs, determining the optimal leading-order program size for general unitary families. Thus, classical randomization achieves the optimal scaling (ν/2+o(1))log_2(1/ε) without requiring coherent quantum memory.
ER -