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arXiv 2402.17693quant-phcs.LO
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具有有限光子数源和探测器的线性光学电路的完备图形语言

A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors

Nicolas Heurtel

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AI总结：

本文提出了一种名为 $\ extbf{LO}_{fi}$-calculus 的完备图形语言，用于在包含有限光子数源和探测器的线性光学电路中推理无限维玻色 Fock 空间，并给出了电路的紧凑通用形式。

摘要：

线性光学电路可用于在光子穿过包括分束器和移相器在内的组件时操纵光子的量子态。这些光子态具有特别高的表达能力，因为它们位于玻色 Fock 空间（一个无限维希尔伯特空间）中。然而，在线性光学量子计算领域，这些基本组件可能不足以高效执行所有感兴趣的计算，例如通用量子计算。为了解决这一限制，通常添加辅助源和探测器，从而能够投影到辅助光子态，进而增加过程的多样性。在本文中，我们引入了 $\ extbf{LO}_{fi}$-calculus，这是一种图形语言，用于对由线性光学的四个核心元素组成的电路进行无限维玻色 Fock 空间上的推理：移相器、分束器以及具有有界光子数的辅助源和探测器。我们提出了一个等式理论，并证明它是完备的：两个 $\ extbf{LO}_{fi}$-circuits 表示相同的量子过程，当且仅当可以通过 $\ extbf{LO}_{fi}$-calculus 的规则将一个转换为另一个。我们给出了此类电路的一种独特且紧凑的通用形式。

英文摘要：

Linear optical circuits can be used to manipulate the quantum states of photons as they pass through components including beam splitters and phase shifters. Those photonic states possess a particularly high level of expressiveness, as they reside within the bosonic Fock space, an infinite-dimensional Hilbert space. However, in the domain of linear optical quantum computation, these basic components may not be sufficient to efficiently perform all computations of interest, such as universal quantum computation. To address this limitation it is common to add auxiliary sources and detectors, which enable projections onto auxiliary photonic states and thus increase the versatility of the processes. In this paper, we introduce the $\textbf{LO}_{fi}$-calculus, a graphical language to reason on the infinite-dimensional bosonic Fock space with circuits composed of four core elements of linear optics: the phase shifter, the beam splitter, and auxiliary sources and detectors with bounded photon number. We present an equational theory that we prove to be complete: two $\textbf{LO}_{fi}$-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the $\textbf{LO}_{fi}$-calculus. We give a unique and compact universal form for such circuits.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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