Faster Born probability estimation via gate merging and frame optimisation

Author:

Koukoulekidis Nikolaos1,Kwon Hyukjoon12,Jee Hyejung H.3,Jennings David14,Kim M. S.1

Affiliation:

1. Department of Physics, Imperial College London, London SW7 2AZ, UK

2. Korea Institute for Advanced Study, Seoul, 02455, Korea

3. Department of Computing, Imperial College London, London SW7 2AZ, UK

4. School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK

Abstract

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+T and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases.

Publisher

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Subject

Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics

Reference67 articles.

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3. R. Jozsa and M. V. den Nest, Quantum Inf. Comput. 14, 633 (2014).

4. D. E. Koh, Quantum Info. Comput. 17, 262–282 (2017).

5. S. Aaronson, A. Bouland, G. Kuperberg, and S. Mehraban (Association for Computing Machinery, New York, NY, USA, 2017) p. 317–327.

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