arXiv:2309.12440 · Physical Review Research

Decomposing large unitaries into multimode devices of arbitrary size

Christian Arends, Lasse L. Wolf, Jasmin D. A. Meinecke, Sonja Barkhofen, Tobias Weich, Tim J. Bartley

Published Feb 29, 2024• 6 citations

Abstract

Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decomposition of an n×n unitary into a product of 2×2 subunitaries (which can for example be realized by beam splitters and phase shifters in linear optics) is well established, we show how for any m>2 this decomposition can be generalized into a product of m×m subunitaries (which can then be realized by a more complex device acting on m modes). If the cost associated with building each m×m multimode device is less than constructing with m(m−1)2 individual 2×2 devices, we show that the decomposition of large unitaries into m×m submatrices is more resource efficient and exhibits a higher tolerance to errors, than its 2×2 counterpart. This allows larger-scale unitaries to be constructed with lower errors, which is necessary for various tasks, not least boson sampling, the quantum Fourier transform, and quantum simulations. Published by the American Physical Society 2024

DOI: 10.1103/physrevresearch.6.l012043

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