Southwest Quantum Information and Technology

A framework for approximating qubit unitaries

Presenting Author: Vadym Kliuchnikov, QuArC (Microsoft)
Contributing Author(s): Jon Yard, Alex Bocharov, Martin Roetteler

We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves ε-approximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+π/12 [arXiv:1409.3552], running on average in time polynomial in O(log(1/ε)) (conditional on a number-theoretic conjecture). Ours is the first such algorithm that works for a wide range of gate sets and provides insight into what should constitute a "good" gate set for a fault-tolerant quantum computer.

Read this article online: http://arxiv.org/abs/1510.03888, http://arxiv.org/abs/1504.04350

(Session 7 : Friday from 11:30 am - 12:00 pm)