Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets
Abstract
We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov, and Mosca [Quantum Inf. Comput. 13(7,8), 607–630 (2013)]. Their algorithm takes as input an exactly synthesizable single-qubit unitary—one which can be expressed without error as a product of Clifford and T gates—and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer n, we consider the "Clifford-cyclotomic" gate set consisting of the Clifford group plus a z-rotation by π/n. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of π/n z-rotations. For the Clifford+T case n = 4, the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring Z[e^(i π/n), 1/2]. We prove that this characterization holds for a handful of other small values of n but the fraction of positive even integers for which it fails to hold is 100%.
Additional Information
© 2015 AIP Publishing LLC. Received 13 February 2015; accepted 9 July 2015; published online 5 August 2015. We thank Jean-Francois Biasse and Michele Mosca for helpful discussions. D.G. and D.M. were supported in part by NSERC. D.G. was supported in part by ARO. IQC is supported in part by the Government of Canada and the province of Ontario.Attached Files
Published - 1.4927100.pdf
Submitted - 1501.04944v1.pdf
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Additional details
- Eprint ID
- 53941
- Resolver ID
- CaltechAUTHORS:20150121-111212393
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Army Research Office (ARO)
- Government of Canada
- Province of Ontario
- Created
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2015-01-21Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter