Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates

2012/06/30 by Vadym Kliuchnikov, Dmitri Maslov, Michele Mosca · 4 citations
Physics and Astronomy · Computer Science · #quant-ph #cs.ET

paper · pdf

published as Quantum Information and Computation, Vol. 13, No. 7,8 pp. 607-630 (2013) · 23 pages, 3 figures, added the proof of T-optimality of the circuits synthesized by Algorithm 1

arxiv created 2013/02/27 · arxiv updated 2013/03/01

Abstract

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring ℤ[(1)/(√(2)),i], in the single-qubit case. We report an efficient synthesis algorithm, with an exact optimality guarantee on the number of Hadamard and T gates used. We conjecture that the equivalence of the sets of unitaries implementable by circuits over the Clifford and T library and unitaries over the ring ℤ[(1)/(√(2)),i] holds in the n-qubit case.

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• Survival of the Optimized: An Evolutionary Approach to T-depth Reduction
• Compact Circuits for Constrained Quantum Evolutions of Sparse Operators

Related

• Synthesis of unitaries with Clifford+T circuits
• Multi-qubit circuit synthesis and Hermitian lattices
• Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries
• The exact synthesis of 1- and 2-qubit Clifford+T circuits
• A framework for exact synthesis