Inverse iteration quantum eigensolvers assisted with a continuous variable

TL;DR

This paper introduces inverse iteration quantum eigensolvers utilizing continuous-variable quantum modes to efficiently find eigenstates of physical systems, demonstrating potential reductions in quantum resource requirements.

Contribution

It proposes a novel quantum eigensolver method that employs continuous-variable resources to implement inverse Hamiltonian operations more efficiently.

Findings

Numerical simulations show effectiveness for molecules and many-body systems.

Continuous-variable resources reduce Hamiltonian evolution time.

Hybrid algorithms compare different Hamiltonian evolution strategies.

Abstract

The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum-classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.