Robust phase estimation of the ground-state energy without controlled time evolution on a quantum device

TL;DR

This paper introduces a method to estimate the ground-state energy of quantum Hamiltonians accurately without controlled time evolution, using adiabatic state preparation and Ramsey measurements, suitable for early quantum devices.

Contribution

The paper presents a novel approach combining ASP and Ramsey measurement to estimate ground-state energy without controlled evolution, enhancing robustness and applicability.

Findings

Accurate energy estimation without controlled time evolution.

Method is robust against non-adiabatic transitions.

Suitable for early fault-tolerant quantum computers.

Abstract

Estimating the ground-state energy of Hamiltonians in quantum systems is an important task. In this work, we demonstrate that the ground-state energy can be accurately estimated without controlled time evolution by using adiabatic state preparation (ASP) and Ramsey-type measurement. By considering the symmetry of the Hamiltonian governing the time evolution during ASP, we can prepare a superposition of the ground state and reference state whose eigenvalue is known. This enables the estimation of the ground-state energy via Ramsey-type measurement. Furthermore, our method is robust against non-adiabatic transitions, making it suitable for use with early fault-tolerant quantum computers and quantum annealing.