Sukin Sim, Harvard University

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Parameterized quantum circuits play an essential role in the performance of many variational hybrid quantum-classical (HQC) algorithms. One challenge in implementing such algorithms is to choose an effective circuit that well-represents the solution space while maintaining a low circuit depth and number of parameters. To characterize and identify expressible yet compact parameterized circuits, we propose several descriptors, including measures of expressibility and entangling capability, that can be statistically estimated from classical simulations of parameterized quantum circuits. We compute these descriptors for different circuit structures, varying the qubit connectivity and selection of gates. From our simulations, we identify circuit fragments that perform well with respect to the descriptors. In particular, we find that two-qubit gates in a ring or all-to-all connected arrangement substantially outperform those on a line. Furthermore, we find that sequences of controlled X-rotation gates consistently achieve better values of the descriptors than sequences of controlled Z-rotation gates. While the correlation between each descriptor and performance of an algorithm remains to be investigated, methods and results from this study can be useful for both algorithm development and design of experiments for general variational HQC algorithms.

Abstract Author(s): Sukin Sim, Peter D. Johnson, Alán Aspuru-Guzik