Efficient approximation of diagonal unitaries over the Clifford+T basis

Abstract

We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+T basis, that minimizes the number of phase-rotation gates in the synthesized approximation circuit. The equivalent T-count of the synthesized circuit is bounded by kC_0 log_2 (1/ε)+E(n, k), where k is the number of distinct phases in the diagonal n-qubit unitary, ε is the desired precision, C0 is a quality factor of the implementation method (1 < C_0 < 4), and E(n, k) is the total entanglement cost (in T gates). We determine an optimal decision boundary in (n, k, ε)-space where our decomposition algorithm achieves lower entanglement cost than previous state-of-the-art techniques. Our method outperforms state-of-the-art techniques for a practical range of ε values and diagonal operators and can reduce the number of T gates exponentially in n when k far less than 2^ n .