Building a large-scale quantum computer with continuous-variable optical technologies

Fukui, Kosuke; Takeda, Shuntaro

doi:10.48550/arxiv.2110.03247

Cited by 2 publications

(2 citation statements)

References 243 publications

(447 reference statements)

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“…CV provides a promising path to scalable, universal and fault-tolerant quantum computing, where one of the bottlenecks is the deterministic implementation of non-Gaussian gates [85]. This bottleneck can be reduced to that of preparing non-Gaussian states through measurement-based constructions [69].…”

Section: Discussion and Open Questionsmentioning

confidence: 99%

Holomorphic representation of quantum computations

Chabaud

Mehraban

2022

Quantum

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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.

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Section: Discussion and Open Questionsmentioning

confidence: 99%

Holomorphic representation of quantum computations

Chabaud

Mehraban

2022

Quantum

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“…CV provides a promising path to scalable, universal and fault-tolerant quantum computing, where one of the bottlenecks is the deterministic implementation of non-Gaussian gates [83]. This bottleneck can be reduced to that of preparing non-Gaussian states through measurement-based constructions [68].…”

Section: Discussion and Open Questionsmentioning

confidence: 99%

Holomorphic representation of quantum computations

Chabaud¹,

Mehraban²

2021

Preprint

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We introduce a model of computing on holomorphic functions, which captures bosonic quantum computing through the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which not only gives a canonical definition 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 introduce formally the model of Holomorphic Quantum Computing. Non-adaptive circuits in this model allow for a classification of subuniversal models that are generalisations of Boson Sampling and Gaussian quantum computing, while adaptive circuits capture existing universal bosonic quantum computing models. Our results leave open the possibility that continuous-variable quantum computations may outperform their discrete-variable counterpart.

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Building a large-scale quantum computer with continuous-variable optical technologies

Cited by 2 publications

References 243 publications

Holomorphic representation of quantum computations

Holomorphic representation of quantum computations

Holomorphic representation of quantum computations

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