Decomposing large unitaries into multimode devices of arbitrary size

TY - JOUR

T1 - Decomposing large unitaries into multimode devices of arbitrary size

AU - Arends, Christian

AU - Wolf, Lasse

AU - Meinecke, Jasmin

AU - Barkhofen, Sonja

AU - Weich, Tobias

AU - Bartley, Tim

PY - 2024/1

Y1 - 2024/1

N2 - 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.

AB - 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.

KW - quant-ph

KW - Quantum Physics

UR - http://www.scopus.com/inward/record.url?scp=85192677174&partnerID=8YFLogxK

U2 - 10.1103/PhysRevResearch.6.L012043

DO - 10.1103/PhysRevResearch.6.L012043

M3 - Journal article

SN - 2643-1564

VL - 6

JO - Physical Review Research

JF - Physical Review Research

IS - 1

M1 - L012043

ER -