PreprintarXiv licencearXiv
Logarithmic-depth quantum simulation of boson sampling
Abstract
We show that boson sampling with an arbitrary m-mode interferometer and n≤ m single-photon inputs can be simulated to inverse-polynomial total-variation error by a logarithmic-depth qubit circuit with polynomially many qubits. The circuit uses Clifford+T gates, arbitrary qubit connectivity, and a single final measurement, and its family is logspace uniform. The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes. This redistribution permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit. Consequently, our result places boson sampling within shallow quantum computation.
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BibTeX
@misc{oh2026logarithmicdepth,
title = {{Logarithmic-depth quantum simulation of boson sampling}},
author = {Changhun Oh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18907},
eprint = {2609.18907},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18907},
}
RIS
TY - UNPB
TI - Logarithmic-depth quantum simulation of boson sampling
AU - Changhun Oh
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18907
UR - https://arxiv.org/abs/2609.18907
AB - We show that boson sampling with an arbitrary m-mode interferometer and n≤ m single-photon inputs can be simulated to inverse-polynomial total-variation error by a logarithmic-depth qubit circuit with polynomially many qubits. The circuit uses Clifford+T gates, arbitrary qubit connectivity, and a single final measurement, and its family is logspace uniform. The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes. This redistribution permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit. Consequently, our result places boson sampling within shallow quantum computation.
ER -