Estimation of many-body quantum Hamiltonians via compressive sensing

Journal Article · Fri Jul 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.84.012107· OSTI ID:22038590

Shabani, A; Rabitz, H ^[1]; Mohseni, M ^[2]; Lloyd, S ^[2]; Kosut, R L ^[3]

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1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)
2. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
3. SC Solutions, Sunnyvale, California 94085 (United States)

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.

• OSTI ID: 22038590
• Journal Information: Physical Review. A, Vol. 84, Issue 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
ATOMS
COMPUTERIZED SIMULATION
FOUR-BODY PROBLEM
HAMILTONIANS
HILBERT SPACE
NUMERICAL ANALYSIS
QUANTUM DOTS