Optimal Estimation of Single Qubit Quantum Evolution Parameters

Alexandr Sergeevich, Stephen D. Bartlett

In this paper we develop qubit Hamiltonian single parameter estimation techniques using Bayesian approach. The algorithms considered are restricted to projective measurements in a fixed basis, and are derived under the assumption that the qubit measurement is much slower than the characteristic qubit evolution. The non-adaptive algorithm is optimized using particle swarm optimization and compared to previously developed locally-optimal scheme.

David C. Collins, Mike Frey

Mădălin Guţǎ, Bas Janssens, Jonas Kahn

Kevin C Young, Mohan Sarovar, Robert L. Kosut +1 more

We consider the problem of quantum multiparameter 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.

Tao, Hong, Xiaoqing Tan

In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multiparameter estimation but it is very difficult. Evolution on SU(N) dynamics is a research method to explore simultaneous multiparameter estimation with the quantum network. As the highly entangled states, graph state, is an intrinsical quantum resource for quantum metrology. For n-qubit graph state, we propose a simultaneous multiparameter estimation scheme that investigates evolution in SU(N) dynamics. For single-parameter estimation, the precision limit beyond the Heisenberg limit in the higher dimension spin of SU(2). We consider two scenarios where the Hamiltonian operator is commutation and non-commutation respectively and verify that the global estimation precision is higher than the local estimation precision. In the parameter limit condition, the precision of parameter estimation for the simultaneous estimation of each parameter is equal to the precision of the singleparameter estimation. In addition, we find a precision-enhancement scheme that depends on the dynamics SU(N). The smaller the N for the dynamics evolution, the higher the precision of the parameter estimation. Finally, we prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multiparameter estimation can attain the quantum Cramér-Rao bound.

Beili Gong, Wei Cui