A qubit update

Charles Q. Choi

J. Allam, A. Matzkin

As per the projection postulate, the evolution of the quantum state of a system upon measurement results in state update. In this work we investigate the characterization of updated states of multipartite entangled qubit states with nondestructive weak measurements, involving weakly coupling a pointer to each qubit while considering a relativistic setup involving different reference frames. As is well known, the updated state at intermediate times is frame dependent and outcome randomness, intrinsic to projective measurements, prevents any information from being acquired on the updated state. Here we will see that when weak measurements are implemented there is instead an interplay between randomness and interference, depending on the number of qubits, so as to maintain consistency between descriptions in arbitrary reference frames. Analytical results are given for a small or infinite number of qubits, while for a finite number of qubits we resort to Monte Carlo sampling in order to simulate numerically the results of weak measurements. As a by-product, we show how a single-shot measurement of the pointers' positions allows us to make quantitative predictions on the outcomes that can be obtained for any observable measured on a distant qubit of the multipartite state.

Xin Li, Huangfu Xu, Xuezhong Guan

To enhance the optimization ability of particle swarm algorithm, a novel quantum-inspired particle swarm optimization algorithm is proposed. In this method, the particles are encoded by the probability amplitudes of the basic states of the multi-qubits system. The rotation angles of multi-qubits are determined based on the local optimum particle and the global optimal particle, and the multi-qubits rotation gates are employed to update the particles. At each of iteration, updating any qubit can lead to updating all probability amplitudes of the corresponding particle. The experimental results of some benchmark functions optimization show that, although its single step iteration consumes long time, the optimization ability of the proposed method is significantly higher than other similar algorithms.

G. Blatter

Graham P. Collins

Takanori Sugiyama, Peter S. Turner, Mio Murao

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance--optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically the performances of two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.