1212.0506 (Brett Giles et al.)

Exact synthesis of multi-qubit Clifford+T circuits    [PDF]

Brett Giles, Peter Selinger

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. We also characterize the Clifford+T operators that can be represented without ancillas.

View original: http://arxiv.org/abs/1212.0506