2015
DOI: 10.48550/arxiv.1510.03888
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A Framework for Approximating Qubit Unitaries

Vadym Kliuchnikov,
Alex Bocharov,
Martin Roetteler
et al.

Abstract: We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves ε-approximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+π/12 [arXiv:1409.3552], running on average in time polynomial in O(log(1/ε)) (conditional on a number-theoretic con… Show more

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Cited by 15 publications
(23 citation statements)
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“…If N T , N √ T and N √ T 3 denote the number of T , √ T and √ T 3 gates used to approximate the rotation, then the algorithm described in [36] finds gate sequences with the number of gates satisfying: 9b.…”
Section: mentioning
confidence: 99%
“…If N T , N √ T and N √ T 3 denote the number of T , √ T and √ T 3 gates used to approximate the rotation, then the algorithm described in [36] finds gate sequences with the number of gates satisfying: 9b.…”
Section: mentioning
confidence: 99%
“…However the gate sets that arise from such general S-arithmetic groups coming from definite quaternion algebras still have reasonably good covering exponents and navigation properties. These have been studied in [KBRY15].…”
Section: -Gates (Inert P )mentioning
confidence: 99%
“…The correspondence between quantum circuits and matrix groups exposes the mathematical structure underlying certain gate sets, thereby enabling exact and efficient manipulation of circuits. These insights, along with applications such as compiling [7,10,12,15,16] and verification [2], motivate the study of the relevant matrix groups.…”
Section: Introductionmentioning
confidence: 99%