Superselection rules and bosonic quantum computational resources
Abstract
We present a method to systematically identify and classify quantum optical non-classical states as classical/non-classical based on the resources they create on a bosonic quantum computer. This is achieved by converting arbitrary bosonic states into multiple modes, each occupied by a single photon, thereby defining qubits of a bosonic quantum computer. Starting from a bosonic classical-like state in a representation that explicitly respects particle number super-selection rules, we apply universal gates to create arbitrary superpositions of states with the same total particle number. The non-classicality of the corresponding states can then be associated to the operations they induce in the quantum computer. We also provide a correspondence between the adopted representation and the more conventional one in quantum optics, where superpositions of Fock states describe quantum optical states, and we identify how multi-mode states can lead to quantum advantage. Our work contributes to establish a seamless transition from continuous to discrete properties of quantum optics while laying the grounds for a description of non-classicality and quantum computational advantage that is applicable to spin systems as well.
Cite
@article{arxiv.2407.03138,
title = {Superselection rules and bosonic quantum computational resources},
author = {Eloi Descamps and Nicolas Fabre and Astghik Saharyan and Arne Keller and Pérola Milman},
journal= {arXiv preprint arXiv:2407.03138},
year = {2024}
}