Abstract

In this talk, I will discuss two newly developed methodologies to reduce the cost of Hamiltonian eigenvalue estimation using quantum computers. The first employs a constant circuit depth variational fast-forwarding representation of the polynomially scaling time-evolution operator to obtain approximate time-evolved states for use in a Krylov subspace expansion. This leads to a substantial reduction in circuit depth with negligible effects on accuracy. The second, a Monte Carlo Projective Quantum Eigensolver (MC-PQE) draws inspiration from conventional Quantum Monte Carlo algorithms to build a methodology which requires orders of magnitude fewer quantum measurements to obtain accurate energy estimates, while also avoiding local minima the Variational Quantum Eigensolver is prone to get caught in. Finally, it reduces the cost of variance-based optimisation methods for excited states to match that of ground state calculations, making it a versatile approach for approximating arbitrary Hamiltonian eigenstates.