Institute for Quantum Computing and Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
Phys Rev Lett. 2009 Dec 18;103(25):250501. doi: 10.1103/PhysRevLett.103.250501.
We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.
我们使用液态核磁共振量子资讯处理器中的 4 个量子位，呈现出逼近琼斯多项式的实验结果。这是首次使用单量子位模型的量子计算确定性量子计算的完整问题的实验实现，该模型使用单个量子位和完全随机状态的寄存器。琼斯多项式是一个纽结不变量，不仅对纽结理论很重要，对统计力学和量子场论也很重要。所实现的演算法是肖尔和乔丹开发的演算法的修改，适用于 NMR 的实现。这些实验结果表明，对于具有四个股线和恰好三个交叉点的纽结的受限情况，91%的时间都可以识别出不同的纽结。
