Nielsen Michael A, Dowling Mark R, Gu Mile, Doherty Andrew C
School of Physical Sciences, University of Queensland, Queensland 4072, Australia.
Science. 2006 Feb 24;311(5764):1133-5. doi: 10.1126/science.1121541.
Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.
量子计算机在解决有趣的计算问题方面极具潜力，但找到能够执行这些复杂任务的高效量子电路仍然是一项挑战。在这里，我们表明，找到最优量子电路本质上等同于在特定弯曲几何结构中找到两点之间的最短路径。通过将寻找量子电路的问题重塑为一个几何问题，我们开辟了利用黎曼几何的数学技术来提出新的量子算法或证明量子计算机能力局限性的可能性。
