Resource-Optimal Single-Qubit Quantum Circuits - Bocharov, Alex; Svore, Krysta M. (Physical Review Letters, 2012)
Determining the optimal implementation of a quantum gate is critical for designing a quantum computer. We consider the crucial task of efficiently decomposing a general single-qubit quantum gate into a sequence of fault-tolerant quantum operations. For a given single-qubit circuit, we construct an optimal gate sequence consisting of fault-tolerant Hadamard (H) and π/8 rotations (T). Our scheme is based on a novel canonical form for single-qubit quantum circuits and the corresponding rules for exactly reducing a general single-qubit circuit to our canonical form. The result is optimal in the number of T gates. We demonstrate that a precomputed epsilon net of canonical circuits in combination with our scheme lowers the depth of approximation circuits by up to 3 orders of magnitude compared to previously reported results.
Also available at http://arxiv.org/pdf/1206.3223v1, and presented at the 12th Asian Quantum Information Science Conference (AQIS).