PreprintCC BY-NC-ND 4.0arXiv
Block encoding of semiseparable matrices via their generators
Abstract
We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an N× N semiseparable matrix with N=2n, the circuit uses 2n+2 ancilla qubits and has O(polylog N) depth, and it realizes a (2√N, 2n+2, 2 √2 ε)-block encoding, where ε is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.
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BibTeX
@misc{antonioli2026block,
title = {{Block encoding of semiseparable matrices via their generators}},
author = {Giacomo Antonioli and Gianna M. Del Corso and Roel Van Beeumen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13228},
eprint = {2610.13228},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13228},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Block encoding of semiseparable matrices via their generators
AU - Giacomo Antonioli
AU - Gianna M. Del Corso
AU - Roel Van Beeumen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13228
UR - https://arxiv.org/abs/2610.13228
AB - We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an N× N semiseparable matrix with N=2^n, the circuit uses 2n+2 ancilla qubits and has O(polylog N) depth, and it realizes a (2√N, 2n+2, 2 √2 ε)-block encoding, where ε is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.
ER -