Quantum State Estimation

Saki Nohara, Ryo Okamoto, Akio Fujiwara +1 more

Accurate estimation of unknown quantum states using limited number of samples is very important but difficult task using fixed measurement basis states since the best local unbiased estimator (LUE) for estimating the parameter depends, in general, on the unknown parameter itself. In order to solve this problem, Nagaoka advocated an adaptive quantum state estimation (AQSE) procedure [1], where the measurement basis states are adaptively selected for each measurement result. Fujiwara proved the strong consistency and asymptotic efficiency for AQSE [2]. Recently, AQSE has been demonstrated by us for the linear polarizations of photons [3]. However, AQSE was designed for a static quantum state, and was not applicable to dynamic states where quantum states change in time. Here, we propose a new protocol, sequential adaptive quantum state estimation (SAQSE) for dynamic quantum states. Our numerical simulation (shown below) clearly show that the estimated value given by SAQSE can follow the true value changing in time whereas AQSE fails. We believe this new protocol will open up the use of quantum state estimation for various applications including biology, e.g. monitoring the motion of fluorescent molecules.

Fei Feng, Peng Zhang, Yifan Zhou +1 more

Quantum power system state estimation (QPSSE) offers an inspiring direction for tackling the challenge of state estimation through quantum computing. Nevertheless, the current bottlenecks originate from the scarcity of practical and scalable QPSSE methodologies in the noisy intermediate-scale quantum (NISQ) era. This paper devises a NISQ-QPSSE algorithm that facilitates state estimation on real NISQ devices. Our new contributions include: (1) A variational quantum circuit (VQC)-based QPSSE formulation that empowers QPSSE analysis utilizing shallow-depth quantum circuits; (2) A variational quantum linear solver (VQLS)-based QPSSE solver integrating QPSSE iterations with VQC optimization; (3) An advanced NISQ-compatible QPSSE methodology for tackling the measurement and coefficient matrix issues on real quantum computers; (4) A noise-resilient method to alleviate the detrimental effects of noise disturbances. The encouraging test results on the simulator and real-scale systems affirm the precision, universality, and scalability of our QPSSE algorithm and demonstrate the vast potential of QPSSE in the thriving NISQ era.

Berthold‐Georg Englert

Sen Kuang

The corresponding quantum state estimation methods and their application backgrounds in four measurement situations are reviewed.The methods involve the typical methods broadly used in experimental quantum field and the state estimation methods which are based on systematic perspective and applicable to quantum feedback control.Eessentially,the estimation principle of every method is explained by stating its development process,and the corresponding analysis and comparison in technology are given.Finally,the quantum state estimation is compared with the corresponding classical state estimation,and some comments on state estimation methods in quantum systems are summarized.