Estimating ground-state properties in quantum simulators with global control

TL;DR

This paper introduces a global control protocol for estimating ground-state energies in quantum simulators, avoiding complex controlled operations and enabling high-precision measurements in analog systems.

Contribution

The authors develop a novel method that uses global time evolution and Loschmidt echo measurements to accurately determine ground-state energies without controlled gates.

Findings

Achieves orders-of-magnitude precision improvement over direct measurements

Demonstrates applicability to 2D Ising and Fermi-Hubbard models

Shows robustness to experimental imperfections and proposes error mitigation

Abstract

Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian. This avoids the need for controlled operations that are typically required in conventional quantum phase estimation and extends the algorithm applicability to analog simulators. Our method extracts energy differences from measurements of the Loschmidt echo over an initial ground-state approximation, combines them with direct energy measurements, and solves a set of equations to infer the individual eigenenergies. We benchmark this protocol on free-fermion systems, showing orders-of-magnitude precision gains over direct energy measurements on the initial state, with accuracy improving rapidly with initial-state fidelity and persisting for hundreds of modes. We further demonstrate applicability to the 2D Ising and Fermi-Hubbard models and show that the approach extends naturally to other observables such as order parameters. Finally, we analyze the effect of experimental imperfections and propose error-mitigation strategies. These results establish a practical route to compute physically relevant quantities with high precision using globally controlled quantum simulators.