Holomorphic representation of quantum computations
Abstract
We study bosonic quantum computations using the SegalBargmann 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 continuousvariable 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 CalogeroMoser particles corresponding to the zeros of the holomorphic function, together with a conformal evolution of Gaussian parameters. We explain that the CalogeroMoser 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 nonGaussian 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.
 Publication:

Quantum
 Pub Date:
 October 2022
 DOI:
 10.22331/q20221006831
 arXiv:
 arXiv:2111.00117
 Bibcode:
 2022Quant...6..831C
 Keywords:

 Quantum Physics
 EPrint:
 60 + 22 pages. Version accepted in Quantum. Comments are welcome!