Optimal quantum multiparameter estimation and application to dipole- and exchange-coupled qubits
Optimal quantum multiparameter estimation and application to dipole- and exchange-coupled qubits
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DOI：
10.1103/physreva.79.062301
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发表时间：
2008-12
影响因子：
2.9
通讯作者：
Kevin C. Young;M. Sarovar;R. Kosut;K. B. Whaley
中科院分区：
文献类型：
--
作者：
Kevin C. Young;M. Sarovar;R. Kosut;K. B. Whaley
我们考虑了带实验约束的量子多参数估计问题，并将其表示为凸优化问题。具体地说，我们概述了一种有效的方法来确定估计量子过程多个未知参数的最优策略，并将该方法应用于一个实际例子。例如，两个电子自旋量子比特通过偶极耦合并交换相互作用，但耦合参数未知--明确地说，两个量子比特之间的位置矢量和交换相互作用的大小是未知的。这种耦合哈密顿量产生了一种么正演化，当它与任意单量子比特操作相结合时，就产生了一套通用的量子门。然而，为了产生高保真的门，未知的参数必须是精确的。我们利用点估计的方差的Cram‘er-Rao界来构造估计这些自由参数的最优实验序列，并对最优实验构形进行了完整的分析.我们将约束最优参数估计问题转化为凸优化问题的方法是有效的，并且对其他系统具有广泛的适用性.
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-fidelity gates. We use the Cram\'er-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.