论文标题
估计琼斯在嘈杂的量子计算机上的多项式
Estimating the Jones polynomial for Ising anyons on noisy quantum computers
论文作者
论文摘要
统一根部对琼斯多项式的评估是量子计算机的范式问题。在这项工作中，我们介绍了从现有的嘈杂量子计算机获得的实验结果，用于该问题的特殊情况，而该问题是经典的杂项。我们的方法依赖于减少评估统一晶格根部的琼斯多项式问题的问题，以计算计算Qudit稳定器电路的量子幅度的问题，这些Qudit稳定器电路通常可以有效地模拟。更具体地说，我们专注于在Unity的第四根词根上进行评估，这是Unity的晶格根部，其中问题减少了评估Qubit稳定器电路振幅的问题。为了估计幅度的真实和虚构部分，我们使用Hadamard测试，产生了非克利福德电路，尽管如此，我们始终可以有效地计算正确的输出。因此，我们进一步认为，该设置定义了近期噪声量子处理器的标准基准。此外，我们研究了通过零噪声外推方法进行量子误差的好处。
The evaluation of the Jones polynomial at roots of unity is a paradigmatic problem for quantum computers. In this work we present experimental results obtained from existing noisy quantum computers for special cases of this problem, where it is classically tractable. Our approach relies on the reduction of the problem of evaluating the Jones polynomial of a knot at lattice roots of unity to the problem of computing quantum amplitudes of qudit stabiliser circuits, which are classically efficiently simulatable. More specifically, we focus on evaluation at the fourth root of unity, which is a lattice root of unity, where the problem reduces to evaluating amplitudes of qubit stabiliser circuits. To estimate the real and imaginary parts of the amplitudes up to additive error we use the Hadamard test, yielding non-Clifford circuits that nevertheless we can always efficiently compute the correct output of. Hence, we further argue that this setup defines a standard benchmark for near-term noisy quantum processors. Additionally, we study the benefit of performing quantum error mitigation with the method of zero noise extrapolation.
