Efficient synthesis of quantum circuits implementing clifford group operations

A note on optimality of quantum circuits over metaplectic basis

Quantum Information and Computation ◽

10.26421/qic18.1-2-1 ◽

2018 ◽

Vol 18 (1&2) ◽

pp. 1-17

Author(s):

Alex Bocharov

Keyword(s):

Quantum Gate ◽

Quantum Circuits ◽

New Method ◽

Clifford Group

Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate R = |0ih0| + |1ih1| − |2ih2|. It is arguably, a ternary basis with the simplest geometry. Recently Cui, Kliuchnikov, Wang and the Author have proposed a compilation algorithm to approximate any twolevel Householder reflection to precision ε by a metaplectic circuit of R-count at most C log3 (1/ε) + O(log log 1/ε) with C = 8. A new result in this note takes the constant down to C = 5 for non-exceptional target reflections under a certain credible numbertheoretical conjecture. The new method increases the chances of obtaining a truly optimal circuit but may not guarantee the true optimality. Efficient approximations of an important ternary quantum gate proposed by Howard, Campbell and others is also discussed.

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Efficient synthesis of probabilistic quantum circuits with fallback

Physical Review A ◽

10.1103/physreva.91.052317 ◽

2015 ◽

Vol 91 (5) ◽

Cited By ~ 25

Author(s):

Alex Bocharov ◽

Martin Roetteler ◽

Krysta M. Svore

Keyword(s):

Quantum Circuits ◽

Efficient Synthesis

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Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits

Physical Review Letters ◽

10.1103/physrevlett.114.080502 ◽

2015 ◽

Vol 114 (8) ◽

Cited By ~ 41

Author(s):

Alex Bocharov ◽

Martin Roetteler ◽

Krysta M. Svore

Keyword(s):

Quantum Circuits ◽

Efficient Synthesis

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Methods for Efficient Synthesis of Large Reversible Binary and Ternary Quantum Circuits and Applications of Linear Nearest Neighbor Model

10.15760/etd.1090 ◽

2000 ◽

Author(s):

Maher Hawash

Keyword(s):

Nearest Neighbor ◽

Quantum Circuits ◽

Efficient Synthesis

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Realization of a new permutative gate library using controlled-kth-root-of-NOT quantum gates for exact minimization of quantum circuits

International Journal of Quantum Information ◽

10.1142/s0219749914500348 ◽

2014 ◽

Vol 12 (05) ◽

pp. 1450034 ◽

Cited By ~ 1

Author(s):

Zhiqiang Li ◽

Xiaoyu Song ◽

Marek Perkowski ◽

Hanwu Chen ◽

Xiaoxia Feng

Keyword(s):

Quantum Logic ◽

Logic Gate ◽

Logic Circuits ◽

Quantum Circuits ◽

Quantum Gates ◽

Quantum Cost ◽

Efficient Synthesis ◽

Quantum Logic Gate ◽

Synthesis Algorithm ◽

Direct Use

Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV+ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV+-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.

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