Abstract
Abstract : This report summarizes our efforts to apply the theory and algorithms of Compressed Sensing (CS) to Quantum Process Tomography (QPT) and Hamiltonian parameter estimation. Specific results include: (1) Development of computational algorithms to include physics based constraints on the quantum process matrix, i.e., positive-semidefinite and trace preserving. (2) Simulations of two-qubit Quantum Fourier Transform interacting with an unknown environment. (3) Establishment of robustness of ideal unitary basis via singular-value-decomposition. (4) The first experimental demonstration of QPT via CS on a photonic system at the University of Queensland. The latter experimental results showed the anticipated and predicted significant reduction of estimation resources, e.g., with respect to an estimate of a 16x16 process matrix obtained from an over complete set of 576 configurations, only 32 configurations were needed to obtain a 97% fidelity, and only 18 configurations to obtain a 94% fidelity. (5) Application of CS to a nearly-sparse many-body Hamiltonian.
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