Decomposing large unitaries into multimode devices of arbitrary size

• URL: http://arxiv.org/abs/2309.12440v1
• Date: Thu, 21 Sep 2023 19:14:39 GMT
• Title: Decomposing large unitaries into multimode devices of arbitrary size
• Authors: Christian Arends, Lasse Wolf, Jasmin Meinecke, Sonja Barkhofen, Tobias Weich and Tim Bartley
• Abstract summary: Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. We show how this decomposition can be generalised into a series of $mtimes m$ multimode devices, where $m>2$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decompostion of an $n\times n$ unitary into a series of $2\times2$ subunitaries is well established (i.e. beamsplitters and phase shifters in linear optics), we show how this decomposition can be generalised into a series of $m\times m$ multimode devices, where $m>2$. If the cost associated with building each $m\times m$ multimode device is less than constructing with $\frac{m(m-1)}{2}$ individual $2\times 2$ devices, we show that the decomposition of large unitaries into $m\times m$ submatrices is is more resource efficient and exhibits a higher tolerance to errors, than its $2\times 2$ 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.

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