dorsal/arxiv
View SchemaOptimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation
| Authors | Robert Kosut, Ian A. Walmsley, Herschel Rabitz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411093 |
| URL | https://arxiv.org/abs/quant-ph/0411093 |
Abstract
A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to quantum process tomography (estimating the Kraus operator sum representation (OSR)), Hamiltonian parameter estimation, and the related problems of state and process (OSR) distribution estimation. Except for Hamiltonian parameter estimation, the other MLE problems are formally of the same type of convex optimization problem and therefore can be solved very efficiently to within any desired accuracy. Associated with each of these estimation problems, and the focus of the paper, is an optimal experiment design (OED) problem invoked by the Cramer-Rao Inequality: find the number of experiments to be performed in a particular system configuration to maximize estimation accuracy; a configuration being any number of combinations of sample times, hardware settings, prepared initial states, etc. We show that in all of the estimation problems, including Hamiltonian parameter estimation, the optimal experiment design can be obtained by solving a convex optimization problem. Software to solve the MLE and OED convex optimization problems is available upon request from the first author.
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"abstract": "A number of problems in quantum state and system identification are\naddressed. Specifically, it is shown that the maximum likelihood estimation\n(MLE) approach, already known to apply to quantum state tomography, is also\napplicable to quantum process tomography (estimating the Kraus operator sum\nrepresentation (OSR)), Hamiltonian parameter estimation, and the related\nproblems of state and process (OSR) distribution estimation. Except for\nHamiltonian parameter estimation, the other MLE problems are formally of the\nsame type of convex optimization problem and therefore can be solved very\nefficiently to within any desired accuracy.\n Associated with each of these estimation problems, and the focus of the\npaper, is an optimal experiment design (OED) problem invoked by the Cramer-Rao\nInequality: find the number of experiments to be performed in a particular\nsystem configuration to maximize estimation accuracy; a configuration being any\nnumber of combinations of sample times, hardware settings, prepared initial\nstates, etc. We show that in all of the estimation problems, including\nHamiltonian parameter estimation, the optimal experiment design can be obtained\nby solving a convex optimization problem.\n Software to solve the MLE and OED convex optimization problems is available\nupon request from the first author.",
"arxiv_id": "quant-ph/0411093",
"authors": [
"Robert Kosut",
"Ian A. Walmsley",
"Herschel Rabitz"
],
"categories": [
"quant-ph"
],
"title": "Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation",
"url": "https://arxiv.org/abs/quant-ph/0411093"
},
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