Efficient synthesis of universal Repeat-Until-Success circuits

2014/04/30 by Alex Bocharov, Martin Roetteler, Krysta M. Svore · 2 citations
Physics and Astronomy · Computer Science · #quant-ph #cs.ET

paper · pdf · doi:10.1103/physrevlett.114.080502

published as Phys. Rev. Lett. 114, 080502 (2015) · 15 pages, 10 figures; reformatted and minor edits; added Fig. 2 to visualize the density of z-rotations implementable via RUS protocols

arxiv created 2014/09/19 · arxiv updated 2015/03/11

Abstract

Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a 2.5 times reduction in expected T-count over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best known algorithm to synthesize RUS circuits requires exponential classical runtime. In this paper we present an algorithm to synthesize an RUS circuit to approximate any given single-qubit unitary within precision ε in probabilistically polynomial classical runtime. Our synthesis approach uses the Clifford+T basis, plus one ancilla qubit and measurement. We provide numerical evidence that our RUS circuits have an expected T-count on average 2.5 times lower than the theoretical lower bound of 3 log₂ (1/ε) for ancilla-free single-qubit circuit decomposition.

Cited by

• Cultivating logical catalysts for fault-tolerant dyadic phase rotations
• Making Neural Networks More Suitable for Approximate Clifford+T Circuit Synthesis

Related

• Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries
• Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries
• Efficient synthesis of probabilistic quantum circuits with fallback
• Synthesis of unitaries with Clifford+T circuits
• Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning