Optimal quantum multi-parameter estimation as applied to dipole- and exchange-coupled qubits Export

@article{citeulike:3837144, abstract = {We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters -- explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelty gates. We use the Cramer-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems.}, archivePrefix = {arXiv}, author = {Young, Kevin C. and Sarovar, Mohan and Kosut, Robert and Whaley, Birgitta K.}, citeulike-article-id = {3837144}, citeulike-linkout-0 = {http://arxiv.org/abs/0812.4635}, citeulike-linkout-1 = {http://arxiv.org/pdf/0812.4635}, day = {26}, eprint = {0812.4635}, keywords = {metrology}, month = {Dec}, posted-at = {2008-12-31 01:51:10}, priority = {2}, title = {Optimal quantum multi-parameter estimation as applied to dipole- and exchange-coupled qubits}, url = {http://arxiv.org/abs/0812.4635}, year = {2008} }

TY - JOUR ID - citeulike:3837144 L3 - citeulike-article-id:3837144 N2 - We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters -- explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelty gates. We use the Cramer-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems. TI - Optimal quantum multi-parameter estimation as applied to dipole- and exchange-coupled qubits KW - metrology AU - Young, Kevin AU - Sarovar, Mohan AU - Kosut, Robert AU - Whaley, Birgitta PY - 2008/Dec/26/ UR - http://arxiv.org/abs/0812.4635 ER -