Process Tomography for Clifford Unitaries

Abstract

We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the asymptotically optimal query complexity. In contrast to previous algorithms that required access to $C^\dagger$ to achieve optimal query complexity, our algorithm achieves the same performance without querying $C^\dagger$. Additionally, we show the algorithm is robust to perturbations and can efficiently learn the closest Clifford to an unknown non-Clifford unitary $U$ using query overhead that is logarithmic in the number of qubits.