Synergy Between Quantum Circuits and Tensor Networks

Jacob Miller
Zapata Computing

Parametrized quantum circuits (PQCs) represent a promising framework for using present-day quantum hardware to solve diverse problems in materials science, quantum chemistry, and machine learning. We introduce a "synergistic" approach that addresses two prominent issues with these models, the prevalence of barren plateaus in PQC optimization landscapes, and the difficulty of outperforming state of the art classical algorithms. This framework first uses classical resources to compute a tensor network (TN) encoding a high-quality solution to a problem of interest, and then converts this classical output into an approximating PQC which can be further improved by the use of quantum resources. Beyond simply boosting the performance of PQC models at initialization, we find this method to significantly reduce the impact of barren plateaus, in a manner that improves with increasing classical computing resources. We believe our results highlight the promise of powerful classical simulation methods not as an obstacle to be overcome in demonstrating practically useful quantum advantage, but rather as a guide to help quantum methods find their way.

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