Decomposing large unitaries into multimode devices of arbitrary size

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Abstract

Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decomposition of an \(n\times n\) unitary into a product of \(2\times 2\) 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 \(m\times m\) subunitaries (which can then be realized by a more complex device acting on \(m\) modes). 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 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.

Citation

@article{AWMBWB24,
  title = {Decomposing large unitaries into multimode devices of arbitrary size},
  author = {Arends, Christian and Wolf, Lasse and Meinecke, Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim J.},
  journal = {Phys. Rev. Res.},
  volume = {6},
  pages = {L012043},
  year = {2024},
  url = {https://link.aps.org/doi/10.1103/PhysRevResearch.6.L012043}
}