2016/08/07 by Carlos A. Riofrío, C. A. Riofrio, D. Gross +9
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Compressed sensing #Computer science #Density matrix #Dimension (graph theory) #Eigenvalues and eigenvectors #Mathematics #Observable #Pauli exclusion principle #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum entanglement #Quantum information #Quantum mechanics #Quantum state #Quantum tomography #Qubit #Realization (probability) #Sparse and Compressive Sensing Techniques #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1038/ncomms15305
published as Nature Comm. 8, 15305 (2017) · 7 pages + 6 page appendix, 36 figures
arxiv created 2016/08/07 · openalex publication_date 2017/05/17 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
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.