Quantum Krylov methods for chemistry and materials science

by Cristian Cortes (Argonne National Laboratory)

Monday Dec 6, 2021, 1:00 PM → 2:00 PM America/Chicago

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Quantum computers promise to deliver accurate results for many important problems in quantum chemistry and materials science. One example is the electronic structure problem which aims to find the ground and excited state energies of a quantum many-body system. In this talk, I will introduce quantum Krylov subspace algorithms which aim to tackle this problem and show how these methods have emerged as a viable alternative to traditional variational quantum algorithms such as VQE. I will present our most recent contributions which develops a unified framework for quantum Krylov-based methods, showing that a wide range of hybrid quantum-classical algorithms can be defined with various trade-offs in terms of quantum and classical algorithm complexity. I will also present a multi-fidelity estimation protocol that avoids the use of the Hadamard test, circumventing the need for controlled multi-qubit gates that can be quite costly for near-term quantum hardware. Our work brings quantum Krylov-based methods to the forefront providing a viable route towards routine quantum advantage demonstrations in chemistry and materials science in the long term.