# Experimental Hamiltonian Learning of An 11-qubit Solid-State Quantum Spin Register

## TL;DR

This paper presents an experimental adaptive method to efficiently learn and validate the Hamiltonian of an 11-qubit solid-state quantum spin system, enabling high-fidelity quantum gate implementation.

## Contribution

It introduces a novel adaptive Hamiltonian learning technique for large quantum systems and demonstrates its effectiveness on an 11-qubit NV center platform.

## Key findings

- Successful Hamiltonian estimation of an 11-qubit system
- High-fidelity universal quantum gates achieved
- Potential for testing quantum algorithms and networking

## Abstract

Learning Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates. However, it is a significant challenge to efficiently characterize the Hamiltonian when its Hilbert space dimension grows exponentially with the system size. Here, we experimentally demonstrate an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single Nitrogen-Vacancy center in a diamond. We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian parameters and demonstrate high-fidelity gates in experiment. Our experimental demonstration shows a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms and to act as a multi-qubit single node in a quantum network.