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Exact synthesis of multiqubit Clifford+T circuits · Around

2012

Exact synthesis of multiqubit Clifford+T circuits

Giles, Brett, Selinger, Peter

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We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[1/sqrt(2),i].

Moreover, we show that one ancilla always suffices.
These facts were conjectured by Kliuchnikov, Maslov, and Mosca.
We obtain an algorithm for synthesizing a exact Clifford+T circuit from any such n-qubit operator.

Built on

Elementary gates for quantum computation
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter · 1995
Earlier work this paper cites.
Générateurs et relations pour les circuits booléens réversibles
J. Musset · 1997
Earlier work this paper cites.

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Quantum Computation and Quantum Information
M. A. Nielsen and I. L. Chuang · 2002
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Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T T gates
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V. Kliuchnikov, D. Maslov, and M. Mosca · 2012
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Then

A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
Original
M. Amy, D. Maslov, M. Mosca, and M. Roetteler · 2012
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Quantum circuits of T T -depth one
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P. Selinger · 2013
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