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Holomorphic representation of quantum computations

Chabaud, Ulysse and Mehraban, Saeed (2022) Holomorphic representation of quantum computations. Quantum, 6 . Art. No. 831. ISSN 2521-327X. doi:10.22331/q-2022-10-06-831.

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We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical description of bosonic quantum computing using basic elements of complex analysis but also provides a unifying picture which delineates the boundary between discrete- and continuous-variable quantum information theory. Using this representation, we show that the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described as an integrable dynamical system of classical Calogero-Moser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the Calogero-Moser dynamics is due to unique features of bosonic Hilbert spaces such as squeezing. We then generalize the properties of this holomorphic representation to the multimode case, deriving a non-Gaussian hierarchy of quantum states and relating entanglement to factorization properties of holomorphic functions. Finally, we apply this formalism to discrete- and continuous- variable quantum measurements and obtain a classification of subuniversal models that are generalizations of Boson Sampling and Gaussian quantum computing.

Item Type:Article
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URLURL TypeDescription
Chabaud, Ulysse0000-0003-0135-9819
Mehraban, Saeed0000-0002-1323-360X
Additional Information:We thank the anonymous referees for their comments. UC acknowledges inspiring discussions with T. Vidick, J. Preskill, S. Ghazi Nezami, P.-E. Emeriau, R. I. Booth, F. Arzani, G. Ferrini, D. Markham, F. Grosshans, and M. Walschaers. SM acknowledges insightful discussions with J. Preskill, T. Vidick, J. Slote and S. Ghazi Nezami. SM gratefully acknowledges the hospitality of the Simons Institute for the theory of computing during Spring 2020 where several basic aspects of this project were motivated. UC and SM acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907).
Group:Institute for Quantum Information and Matter
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Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Record Number:CaltechAUTHORS:20230119-174769800.2
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ID Code:118864
Deposited By: Research Services Depository
Deposited On:07 Feb 2023 20:02
Last Modified:07 Feb 2023 20:02

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