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Representation of Quantum Circuits with Clifford and $\pi/8$ Gates · Around

2008

Representation of Quantum Circuits with Clifford and $\pi/8$ Gates

Matsumoto, Ken, Amano, Kazuyuki

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In this paper, we introduce the notion of a normal form of one qubit quantum circuits over the basis $\{H, P, T\}$, where $H$, $P$ and $T$ denote the Hadamard, Phase and $\pi/8$ gates, respectively.

This basis is known as the {\it standard set} and its universality has been shown by Boykin et al.
[FOCS '99].
Our normal form has several nice properties: (i) Every circuit over this basis can easily be transformed into a normal form, and (ii) Every two normal form circuits compute same unitary matrix if and only if both circuits are identical.

Built on

P. Shor, “Algorithms for Quantum Computation: Discrete Logarithms and Factoring”, Proc. 35th FOCS
Original
1994
Earlier work this paper cites.
P. O. Boykin, T. Mor, M. Pulver, V. P. Roychowdhury, F. Vatan, “On Universal and Fault-Tolerant Quantum Computing: A Novel Basis and a New Constructive Proof of Universality for Shor’s Basis”, Proc. 40th FOCS
1999
Earlier work this paper cites.

Similar

M. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information
2000
Cited alongside, same era.
S. Aaronson, D. Gottesman, “Improved Simulation of Stabilizer Circuits”, Physical Review A, 70:052328 (2004)
2004
Cited alongside, same era.
M. B. Elliott, B. Eastin, and C. M. Caves “Graphical description of the action of Clifford operators on stabilizer states”, quant-ph/0703278
Cited in the paper.

Then

H. Buhrman, R. Cleve, M. Laurent, N. Linden, A. Schrijver and F. Unger, “New Limits on Fault-Tolerant Quantum Computation”, Proc. 47th FOCS
2006
Later among the works it cites.
C. M. Dawson, M. A. Nielsen, “The Solovey-Kitaev Algorithm”, Quantum Inf. Comput
2006
Later among the works it cites.

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