Estimating Jones and Homfly polynomials with one clean qubit
Estimating Jones and Homfly polynomials with one clean qubit
复制标题
用一个干净的量子位估计 Jones 和 Homfly 多项式
DOI：
10.26421/qic9.3-4-6
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
P. Wocjan
中科院分区：
文献类型：
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作者：
S. Jordan;P. Wocjan
琼斯多项式和HOMFLY多项式是与量子计算密切相关的环节不变量。最近的研究表明，对于一个干净的量子比特复杂度类[18]来说，在单位的五根处找到辫的迹闭的琼斯多项式的某个近似是一个完全的问题。这是在量子计算机上在多项式时间内可解决的一类问题，作用于一个量子位纯而其余量子位最大程度混合的初始状态。在这里，我们推广了这一结果，表明一台干净的量子比特计算机可以有效地近似辫在任何单位根处的迹闭的琼斯多项式和单变量homfly多项式。
The Jones and HOMFLY polynomials are link invariants with close connections to quan-tum computing. It was recently shown that finding a certain approximation to the Jonespolynomial of the trace closure of a braid at the fifth root of unity is a complete problemfor the one clean qubit complexity class[18]. This is the class of problems solvable inpolynomial time on a quantum computer acting on an initial state in which one qubitis pure and the rest are maximally mixed. Here we generalize this result by showingthat one clean qubit computers can efficiently approximate the Jones and single-variableHOMFLY polynomials of the trace closure of a braid at any root of unity.