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Real-time Subspace Methods for Hamiltonian Eigenvalue Estimation on Quantum Hardware

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If you have a question about this talk, please contact Maria-Andreea Filip.

One of the most promising expected applications of near-term quantum computers lies in the study of static and dynamical properties of quantum many-body systems. Many quantum computing algorithms have been proposed with this goal in mind, with a focus on Hamiltonian eigenvalue extraction, a problem central to chemistry, physics, and materials science. However, the majority of established quantum algorithms require a prohibitively large number of resources for near-term hardware.

Here we describe the variational quantum phase estimation (VQPE) method, a compact and efficient real-time subspace algorithm to extract eigenvalues using quantum hardware. We theoretically and numerically explore a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, applicable to the VQPE algorithm as well as others. We discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

This talk is part of the Lennard-Jones Centre series.

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