# Quantum Non-demolition Measurement of a Many-Body Hamiltonian

## TL;DR

This paper demonstrates a quantum non-demolition measurement technique for the Hamiltonian of a complex many-body system using trapped-ion quantum simulators, enabling the study of fundamental physics phenomena.

## Contribution

It introduces a novel QND measurement scheme for many-body Hamiltonians, extending quantum measurement capabilities to complex systems in quantum simulation.

## Key findings

- Single-shot measurement of many-body energy eigenstates
- Preparation of the system in a narrow energy band
- Framework for exploring statistical physics principles

## Abstract

In an ideal quantum measurement, the wave function of a quantum system collapses to an eigenstate of the measured observable, and the corresponding eigenvalue determines the measurement outcome. If the observable commutes with the system Hamiltonian, repeated measurements yield the same result and thus minimally disturb the system. Seminal quantum optics experiments have achieved such quantum non-demolition (QND) measurements of systems with few degrees of freedom. In contrast, here we describe how the QND measurement of a complex many-body observable, the Hamiltonian of an interacting many-body system, can be implemented in a trapped-ion analog quantum simulator. Through a single-shot measurement, the many-body system is prepared in a narrow band of (highly excited) energy eigenstates, and potentially even a single eigenstate. Our QND scheme, which can be carried over to other platforms of quantum simulation, provides a framework to investigate experimentally fundamental aspects of equilibrium and non-equilibrium statistical physics including the eigenstate thermalization hypothesis and quantum fluctuation relations.