Process Tomography for Clifford Unitaries

TL;DR

This paper introduces an optimal quantum process tomography algorithm for Clifford unitaries using Bell basis measurements, achieving minimal query complexity without needing the inverse operation, and extends to approximate non-Clifford unitaries.

Contribution

The authors develop a deterministic, optimal-query quantum process tomography algorithm for Clifford unitaries that does not require access to the inverse operation, unlike previous methods.

Findings

Achieves asymptotically optimal query complexity of 4n+3 for Clifford unitaries.

Does not require querying the inverse of the unitary, simplifying implementation.

Can efficiently approximate the closest Clifford to a non-Clifford unitary with logarithmic query overhead.

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.