Monitoring Quantum Simulators via Quantum Non-Demolition Couplings to Atomic Clock Qubits

TL;DR

This paper proposes a method to monitor the energy evolution of quantum simulators using quantum non-demolition couplings to atomic clock qubits, enabling spectral analysis and eigenstate preparation.

Contribution

It introduces a physical implementation of QND couplings in Rydberg atom arrays and applies this to measure spectral properties and eigenstates of quantum many-body systems.

Findings

Demonstrates a protocol for spectral form factor measurement.

Shows feasibility of energy eigenstate preparation on Rydberg platforms.

Provides a framework for quantum phase estimation in analog simulators.

Abstract

We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic vs. non-ergodic dynamics, which we illustrate for disordered 1D Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies, and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.