An algorithm for the T-count
(pp1261-1276)
David
Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo
doi:
https://doi.org/10.26421/QIC14.15-16-1
Abstracts:
We consider quantum circuits composed of Clifford and T gates. In this
context the T gate has a special status since it confers universal
computation when added to the (classically simulable) Clifford gates.
However it can be very expensive to implement fault-tolerantly. We
therefore view this gate as a resource which should be used only when
necessary. Given an n-qubit unitary U we are interested in computing a
circuit that implements it using the minimum possible number of T gates
(called the T-count of U). A related task is to decide if the T-count of
U is less than or equal to m; we consider this problem as a function of
N = 2n and m. We provide a classical algorithm which solves it using
time and space both upper bounded as O(Nmpoly(m, N)). We implemented our
algorithm and used it to show that any Clifford+T circuit for the
Toffoli or the Fredkin gate requires at least 7 T gates. This implies
that the known 7 T gate circuits for these gates are T-optimal. We also
provide a simple expression for the T-count of single-qubit unitaries.
Key words:
circuit synthesis, Clifford gates, T gates, unitary |