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Title: Optimal ancilla-free Pauli+V circuits for axial rotations

We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL{sub 2}(ℤ) geometry is almost elementary.
Authors:
 [1] ; ;  [2]
  1. Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043 (United States)
  2. Microsoft Research, Redmond, Washington 98052 (United States)
Publication Date:
OSTI Identifier:
22479568
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; APPROXIMATIONS; FACTORIZATION; GEOMETRY; MATRICES; PAULI SPIN OPERATORS; QUANTUM COMPUTERS