Estimation of many-body quantum Hamiltonians via compressive sensing

We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one c...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2011-07, Vol.84 (1), Article 012107
Main Authors: Shabani, A., Mohseni, M., Lloyd, S., Kosut, R. L., Rabitz, H.
Format: Article
Language:English
Subjects:
ALGORITHMS
ATOMS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMPUTERIZED SIMULATION
FOUR-BODY PROBLEM
HAMILTONIANS
HILBERT SPACE
NUMERICAL ANALYSIS
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM DOTS
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Summary:We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental configurations, consisting of random local preparations and measurements, one can estimate the Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly s sparse in a known basis. The classical postprocessing is a convex optimization problem on the total Hilbert space which is generally not scalable. We numerically simulate the performance of this algorithm for three- and four-body interactions in spin-coupled quantum dots and atoms in optical lattices. Furthermore, we apply the algorithm to characterize Hamiltonian fine structure and unknown system-bath interactions.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.84.012107