A Near-Term Quantum Algorithm for Computing Molecular and Materials Properties based on Recursive Variational Series Methods

Abstract

Determining properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is: how might we use imperfect near-term quantum computers to solve problems of practical value? We propose a quantum algorithm to estimate properties of molecules using near-term quantum devices. The method is a recursive variational series estimation method, where we expand an operator of interest in terms of Chebyshev polynomials, and evaluate each term in the expansion using a variational quantum algorithm. We test our method by computing the one-particle Green's function in energy domain and the autocorrelation function in time domain, finding some advantages to this approach over existing methods.

Calculating the many-body density of states on a digital quantum computer

“…Block encoding of a Hamiltonian is deeply connected with the Chebyshev polynomials [30], implementing the Hamiltonian as a quantum walk as exploited in the context of the KPM in [31] and more generally to estimate physical properties in [32,33]. An alternative is to compute the Chebyshev moments iteratively in a variational quantum algorithm [34] or otherwise overcoming the problem of implementing the Chebyshev polynomials using suitably defined Fourier ones [35,36].…”