Asymptotically Optimal Topological Quantum Compiling

作者：Kliuchnikov Vadym^*; Bocharov Alex; Svore Krysta M

来源：Physical Review Letters, 2014, 112(14): 140504.

DOI：10.1103/PhysRevLett.112.140504

We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between 10(-10) and 10(-30).

• 出版日期2014-4-9
• 单位Microsoft