Quantum Circuit Design using Matrix Decomposition and its application

我们提出了以下算法和应用：1)扩展Clifford群的高效量子算法及其在离散对数问题中的应用。2)高效的矩阵分解算法。3)在量子数组上构造高效量子电路的矩阵分解算法。4)一种高效的量子电路等价性验证算法。5)BDD的量子版本DDMF及其在构造大规模量子电路中的应用。6)关于量子下推自动机计算复杂性类的一个新结果。7)一种在LNN上将正常量子电路转换为有效量子电路的算法。8)使用量子行走解决SAT问题的高效算法。

We proposed the following algorithms and applications: 1) Efficient quantum algorithms for the extended Clifford group and its application to the discrete logarithm problem. 2) An efficient matrix decomposition algorithm. 3) A matrix decomposition algorithm that constructs efficient quantum circuit on qudits. 4) An efficient equivalence checking algorithm of quantum circuits. 5) DDMF, a quantum version of BDD, and its application to constructing large-scale quantum circuits. 6) A new result about computational complexity class of quantum pushdown automata. 7) An algorithm that converts normal quantum circuits to efficient quantum circuits on LNN. 8) An efficient algorithm that solves SAT problems using quantum walk.