Quantum Gaussian filter for exploring ground-state properties

TL;DR

This paper introduces a quantum Gaussian filter (QGF) method that uses a hybrid quantum-classical approach to efficiently project quantum states onto target states, with applications demonstrated on the quantum Ising model.

Contribution

The paper presents a novel quantum Gaussian filter algorithm that is more flexible and resource-efficient, utilizing classical optimization and postprocessing, and introduces a full quantum implementation with an ancillary mode.

Findings

Demonstrated the QGF on the quantum Ising model with numerical simulations under noise.

Showed the flexibility of the method with classical optimization of coefficients.

Proposed a full quantum approach using an ancillary continuous-variable mode.

Abstract

Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian function of the system Hamiltonian. A hybrid quantum-classical algorithm feasible on near-term quantum computers is developed, which implements the quantum Gaussian filter as a linear combination of Hamiltonian evolution at various times. Remarkably, the linear combination coefficients are determined classically and can be optimized in the postprocessing procedure. Compared to the existing filter algorithms whose coefficients are given in advance, our method is more flexible in practice under given quantum resources with the help of postprocessing on classical computers. We demonstrate the quantum Gaussian filter algorithm for the quantum Ising model with numeral simulations under noises. We also propose an alternative full quantum approach that implements a QGF with an ancillary continuous-variable mode.