Multinomial shot sampling for quantum circuits
Abstract
In classical simulations of quantum circuits, sampling shots (measurement outcomes) from the final state is a routine but costly step. In widely used software, including Qiskit and PennyLane, its cost grows linearly with the number of shots S, even when the simulation has already produced the full state vector, because every shot is generated and processed individually. If only the measurement counts are needed, this is unnecessary. The counts can be drawn directly from a multinomial distribution, decomposed into a sequence of conditional binomial draws, each performed in expected constant time by the BTPE algorithm. The sampling cost is then independent of S. We describe an implementation of this approach, which also shortens the computation for states whose probability is concentrated on a few outcomes, and compare it with Qiskit's sampling primitives for up to 20 qubits and 106 shots. Our implementation is faster in every configuration tested, by a factor that grows with the number of shots and exceeds 103 in most configurations at S = 106, and its samples are statistically indistinguishable from those of the reference implementations.
Related
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BibTeX
@misc{mohammad2026multinomial,
title = {{Multinomial shot sampling for quantum circuits}},
author = {Ijaz Ahamed Mohammad and Daniel Nagaj and Martin Plesch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35119},
eprint = {2610.35119},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35119},
}
RIS
TY - UNPB
TI - Multinomial shot sampling for quantum circuits
AU - Ijaz Ahamed Mohammad
AU - Daniel Nagaj
AU - Martin Plesch
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35119
UR - https://arxiv.org/abs/2610.35119
AB - In classical simulations of quantum circuits, sampling shots (measurement outcomes) from the final state is a routine but costly step. In widely used software, including Qiskit and PennyLane, its cost grows linearly with the number of shots S, even when the simulation has already produced the full state vector, because every shot is generated and processed individually. If only the measurement counts are needed, this is unnecessary. The counts can be drawn directly from a multinomial distribution, decomposed into a sequence of conditional binomial draws, each performed in expected constant time by the BTPE algorithm. The sampling cost is then independent of S. We describe an implementation of this approach, which also shortens the computation for states whose probability is concentrated on a few outcomes, and compare it with Qiskit's sampling primitives for up to 20 qubits and 10^6 shots. Our implementation is faster in every configuration tested, by a factor that grows with the number of shots and exceeds 10^3 in most configurations at S = 10^6, and its samples are statistically indistinguishable from those of the reference implementations.
ER -