title: Efficient synthesis of universal repeat-until-success quantum circuits.
abstract: Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approximate any given single-qubit unitary to precision ϵ over the Clifford+T basis. Surprisingly, the T count of the synthesized RUS circuit surpasses the theoretical lower bound of 3 log_{2}(1/ϵ) that holds for purely unitary single-qubit circuit decomposition. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected T count of 1.15 log_{2}(1/ϵ) for single-qubit z rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher density in the space of all unitaries compared to the density of purely unitary implementations.
authors.affiliation: Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Bocharov
authors.affiliation: Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Roetteler
authors.affiliation: Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA.
authors.forename: Krysta M
authors.initials: KM
authors.lastname: Svore