Quantum Bootstrapping via Compressed Quantum Hamiltonian Learning

TL;DR

This paper introduces a quantum bootstrapping protocol that leverages small quantum simulators and Bayesian inference to efficiently characterize and control larger quantum systems, surpassing traditional short-time evolution methods.

Contribution

It presents a novel method combining quantum simulation, Bayesian inference, and Lieb-Robinson bounds for scalable quantum system characterization and control.

Findings

An 8-qubit simulator calibrates a 50-qubit system with minimal data.

The protocol outperforms short-time evolution methods in efficiency.

Numerical results demonstrate effective control of large quantum systems.

Abstract

Recent work has shown that quantum simulation is a valuable tool for learning empirical models for quantum systems. We build upon these results by showing that a small quantum simulators can be used to characterize and learn control models for larger devices for wide classes of physically realistic Hamiltonians. This leads to a new application for small quantum computers: characterizing and controlling larger quantum computers. Our protocol achieves this by using Bayesian inference in concert with Lieb-Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. Whereas Fisher information analysis shows that current methods which employ short-time evolution are suboptimal, interactive quantum learning allows us to overcome this limitation. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8-qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data.