Asymptotically optimal topological quantum compiling.
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).
Institute for Quantum Computing and David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Vadym
V
Kliuchnikov
Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
Alex
A
Bocharov
Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
Krysta M
KM
Svore