Exact synthesis of multiqubit Clifford+T circuits
Brett Giles and Peter Selinger
Accepted
We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local 1 ancillas if and only if its entries are in the ring Z[1/2,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.