Experimental quantum compressed sensing for a seven-qubit system

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.

Quantum compressed sensing can provide a scalable way to characterize quantum states and devices, but has been so far limited to states with quickly decaying eigenvalues. Here the authors show that it can be appropriate even in the general case, demonstrating reconstruction the state of a seven-qubit system.

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

Unitary transformations are the most general input-output maps available in closed quantum systems. Good control protocols have been developed for qubits, but questions remain about the use of optimal control theory to design unitary maps in high-dimensional Hilbert spaces, and about the feasibility of their robust implementation in the laboratory. Here we design and implement unitary maps in a 16-dimensional Hilbert space associated with the 6S(1/2) ground state of (133)Cs, achieving fidelities >0.98 with built-in robustness to static and dynamic perturbations. Our work has relevance for quantum information processing and provides a template for similar advances on other physical platforms.

Quantum control in the Cs 6S(1/2) ground manifold using radio-frequency and microwave magnetic fields

We implement arbitrary maps between pure states in the 16-dimensional Hilbert space associated with the ground electronic manifold of ^{133}Cs. This is accomplished by driving atoms with phase modulated radio-frequency and microwave fields, using modulation waveforms found via numerical optimization and designed to work robustly in the presence of imperfections. We evaluate the performance of a sample of randomly chosen state maps by randomized benchmarking, obtaining an average fidelity >99%. Our protocol advances state-of-the-art quantum control and has immediate applications in quantum metrology and tomography.