论文标题
克利福德电路及以后的象征性合成
Symbolic Synthesis of Clifford Circuits and Beyond
论文作者
论文摘要
路径总和是用于量子操作的方便符号形式主义，并应用了量子协议的仿真，优化和验证。与量子电路不同，路径总和不限于单一操作，而是可以表达任意线性的操作。因此，在路径总和研究中自然出现了两个问题：单位性问题和提取问题。前者是确定给定路径总和是否代表统一操作员的问题。后者是构建量子电路的问题，鉴于有望代表统一操作员的路径总和。 在本文中，我们表明单位性问题一般是共同的，但是当限于Clifford路径总和时，它在P中。然后，我们提供一种算法来从统一的Clifford路径总和合成Clifford电路。我们的提取算法产生的电路是C1-H-C2的形式，其中C1和C2是无HADAMARD的电路，H是Hadamard大门的一层。我们还提供了提取算法对任意路径总和的启发式概括。尽管不能保证该算法成功，但通常会成功并通常会产生自然的电路。除了应用量子电路的优化和分解外，我们还通过直接从路径总和合成标准量子傅立叶变换来证明算法的能力。
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can express arbitrary linear ones. Two problems, therefore, naturally arise in the study of path sums: the unitarity problem and the extraction problem. The former is the problem of deciding whether a given path sum represents a unitary operator. The latter is the problem of constructing a quantum circuit, given a path sum promised to represent a unitary operator. In this paper, we show that the unitarity problem is co-NP-hard in general, but that it is in P when restricted to Clifford path sums. We then provide an algorithm to synthesize a Clifford circuit from a unitary Clifford path sum. The circuits produced by our extraction algorithm are of the form C1-H-C2, where C1 and C2 are Hadamard-free circuits and H is a layer of Hadamard gates. We also provide a heuristic generalization of our extraction algorithm to arbitrary path sums. While this algorithm is not guaranteed to succeed, it often succeeds and typically produces natural looking circuits. Alongside applications to the optimization and decompilation of quantum circuits, we demonstrate the capability of our algorithm by synthesizing the standard quantum Fourier transform directly from a path sum.
