Erlangen 2018 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 46: Quantum Information (Concepts and Methods) IV

Q 46.7: Vortrag

Mittwoch, 7. März 2018, 15:30–15:45, K 1.019

Recovery of quantum gates from few average gate fidelities — •Ingo Roth¹, Richard Kueng², Shelby Kimmel³, Yi-Kai Liu⁴, Jens Eisert¹, and Martin Kliesch⁵ — ¹FU Berlin, Germany — ²CalTech, USA — ³Middlebury College, USA — ⁴NIST, Gaithersburg, USA — ⁵University of Gdańsk, Poland

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 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(d⁴) average gate fidelities allow to uniquely determine a unital quantum channel acting on a d-dimenisonal Hilbert space. For the important case of characterizing multi-qubit unitary gates, we can further reduce this number to O(d² 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.