确定性量子计算的线性光学方案的代数方法
An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing
摘要：
线性光学无源（LOP）器件和光子计数器足以实现单光子的通用量子计算，并且已经提出了特定的方案。本文讨论LOP变换的代数结构与量子计算之间的联系。我们首先展示了如何将N个光学模式的Fock空间分解为有限维子空间，这些子空间适合于编码量子比特串并且在LOP变换下不变（这些子空间与U（N）的不可约酉表示空间有关）。接下来，我们将展示如何以算法方式设计LOP电路，它确定性地实现任何量子线路。我们也提出了一些简单的例子，如电路实现CNOT门和贝尔状态发生器/分析器。
英文摘要：
Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.
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