Recovery of Quantum Gates from Few Average Gate Fidelities
January 10th, 2018 MARTIN KLIESCH University of Gdańsk

An important task in quantum information science is the characterization of quantum processes, but achieving this characterization efficiently and accurately is often a challenge. In this work, we consider average gate fidelities as data to characterize quantum gates. Average gate fidelities are routinely measured in a number of experimental setups and promise robustness against state preparation and measurement errors.

We show that any unital quantum channel can be affinely expanded in terms of any given unitary 2-design with coefficients determined by the average gate fidelities. Therefore O(d^4) average gate fidelities allow to uniquely determine a unital quantum channel in Hilbert space dimension d.

For the important case of characterizing multi-qubit unitary gates, we further reduce this number to O(d^2 \log (d)) average gate fidelities measured with respect to random Clifford gates, which are natural for many experiments.

The proofs rely on compressed sensing techniques and new representation theoretic results on the Clifford group.

Seminar, January 10, 2018, 12:00. ICFO’s Seminar Room

Hosted by Prof. Antonio Acín