IQI Weekly Seminar
Abstract: One of the core tasks in quantum information science is the characterisation of quantum processes, but achieving this characterisation efficiently and accurately is a challenge. In this work, we consider using data from average gate fidelities to characterize quantum gates. Average gate fidelities are relatively easy to learn, and in some cases have additional robustness to state preparation and measurement errors. We prove that O(d^4) average gate fidelities suffice to fully characterise any unital quantum channel. For the important case of characterizing multi-qubit unitary gates, we can further reduce this number to O(d^2 log (d)) average fidelities measured with respect to random Clifford gates, which are natural for many experiments. As a side result, we also obtain a novel statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a noise process.
In our proofs we exploit new representation theoretic insights on the Clifford group, develop a version of Collins' calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.