We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids. The algorithm evaluates the Tutte polynomial recursively using the deletion–contraction property while attempting to exploit structural properties of the matroid. We consider several variations of our algorithm and present experimental results comparing their performance on two classes of random quantum circuits. Further, we obtain an explicit form for Clifford circuit amplitudes in terms of matroid invariants and an alternative efficient classical algorithm for computing the output probability amplitudes of Clifford circuits.

我们建立了一个经典的启发式算法来精确计算量子概率幅度。我们的算法基于将量子电路的输出概率幅度映射到图形拟阵的 Tutte 多项式的评估。该算法在尝试利用拟阵的结构特性的同时，使用删除-收缩特性递归地评估 Tutte 多项式。我们考虑了我们算法的几种变体，并展示了比较它们在两类随机量子电路上的性能的实验结果。此外，我们根据拟阵不变量获得了 Clifford 电路幅度的显式形式，以及用于计算 Clifford 电路输出概率幅度的替代有效经典算法。