Efficient synthesis of universal repeat-until-success quantum circuits

Physical Review Letters
Alex BocharovKrysta M Svore

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.

References

Dec 12, 2012·Physical Review Letters·Alex Bocharov, Krysta M Svore

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Citations

Mar 19, 2016·Physical Review Letters·Mario KrennAnton Zeilinger
Apr 5, 2018·Scientific Reports·Taewan Kim, Byung-Soo Choi
Jul 22, 2018·Physical Review Letters·David PoulinMatthias Troyer
Feb 25, 2017·Physical Review Letters·Earl T Campbell, Mark Howard
Dec 18, 2020·Journal of Chemical Theory and Computation·Nicholas P BaumanKarol Kowalski

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