Abstract
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the experimental realisation of such a protocol is impeded by the large effort required to estimate the fidelity of an implemented gate. With a hierarchy of approximations we find a faithful approximation to the quantum process fidelity that can be estimated experimentally with reduced effort. Its practical use is demonstrated with the optimisation of a three-qubit quantum gate on a commercially available quantum processor.
Highlights
Experimental progress in developing quantum computers has led to the realization of noisy intermediate scale quantum (NISQ) devices in a wide array of experimental platforms [1,2,3,4]
Quantum channels may be directly optimized such that the resulting channel produces a much more faithful implementation of the desired dynamics
Direct process fidelity estimation would be a natural choice for this; its implementation on NISQ hardware is rendered impractical through the requirement that the input state and measurement basis be changed at every shot of an experiment
Summary
Experimental progress in developing quantum computers has led to the realization of noisy intermediate scale quantum (NISQ) devices in a wide array of experimental platforms [1,2,3,4]. A number of techniques have been developed for error mitigation in quantum computations, wherein additional measurement data and classical postprocessing are used in order to extract relatively noise-free results from the noisy devices [7,8,9,10]. In this work we introduce a hierarchy of approximations to the process fidelity which we refer to as k fidelities These are given in terms of a physically implementable set of expectation values which, together with the fact they are approximately monotonic functions of the process fidelity, means they have the potential to provide alternative figures of merit by which the quality of quantum channels may be assessed. We demonstrate the superior performance of the 0 fidelity estimations under these conditions both numerically and through experiments performed on an IBM quantum device
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