Experimental quantum compressed sensing for a seven-qubit system

TL;DR

This paper demonstrates the first experimental implementation of quantum compressed sensing for a seven-qubit system, enabling efficient state reconstruction with incomplete data and introducing scalable numerical methods.

Contribution

It presents the largest-scale experimental quantum compressed sensing implementation and new numerical techniques for scalable quantum state reconstruction.

Findings

Successful reconstruction of a seven-qubit state from incomplete measurements

Validation of low-rank approximation in noisy, high-dimensional quantum states

Demonstration of efficient tomography in a trapped ion quantum computer

Abstract

Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum device---scales unfavorably to the point that state-of-the-art systems can no longer be treated. Quantum compressed sensing mitigates this problem by reconstructing the state from an incomplete set of observables. In this work, we present an experimental implementation of compressed tomography of a seven qubit system---the largest-scale realization to date---and we introduce new numerical methods in order to scale the reconstruction to this dimension. Originally, compressed sensing has been advocated for density matrices with few non-zero eigenvalues. Here, we argue that the low-rank estimates provided by compressed sensing can be appropriate even in the general case. The reason is that statistical noise often allows only for the leading eigenvectors to be reliably reconstructed: We find that the remaining eigenvectors behave in a way consistent with a random matrix model that carries no information about the true state. We report a reconstruction of quantum states from a topological color code of seven qubits, prepared in a trapped ion architecture, based on tomographically incomplete data involving 127 Pauli basis measurement settings only, repeated 100 times each.