Experimental quantum compressed sensing for a seven-qubit system

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 reconstruction of states and processes of a quantum device - scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system - a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete - 127 Pauli basis measurement settings - and highly noisy - 100 repetitions each - regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state.