Periodic Modulation Effect on Self-Trapping of Two weakly coupled Bose-Einstein Condensates

With phase space analysis approach, we investigate thoroughly the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BEC) in a symmetric double-well potential. We identify two kinds of self-trapping by their different relative phase behavior. With applying a periodic modulation on the energy bias of the system we find the occurrence of the self-trapping can be controlled, saying, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high and low frequency modulations. For an intermediate frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affects the tunnelling dynamics and demonstrate many novel phenomena. Finally, we study the effects of many-body quantum fluctuation on self-trapping and discuss the possible experimental realization of the model.Comment: 7 pages, 11 figure

Verifying Fairness in Quantum Machine Learning

Due to the beyond-classical capability of quantum computing, quantum machine learning is applied independently or embedded in classical models for decision making, especially in the field of finance. Fairness and other ethical issues are often one of the main concerns in decision making. In this work, we define a formal framework for the fairness verification and analysis of quantum machine learning decision models, where we adopt one of the most popular notions of fairness in the literature based on the intuition -- any two similar individuals must be treated similarly and are thus unbiased. We show that quantum noise can improve fairness and develop an algorithm to check whether a (noisy) quantum machine learning model is fair. In particular, this algorithm can find bias kernels of quantum data (encoding individuals) during checking. These bias kernels generate infinitely many bias pairs for investigating the unfairness of the model. Our algorithm is designed based on a highly efficient data structure -- Tensor Networks -- and implemented on Google's TensorFlow Quantum. The utility and effectiveness of our algorithm are confirmed by the experimental results, including income prediction and credit scoring on real-world data, for a class of random (noisy) quantum decision models with 27 qubits ($2^{27}$-dimensional state space) tripling ($2^{18}$ times more than) that of the state-of-the-art algorithms for verifying quantum machine learning models

Detecting Violations of Differential Privacy for Quantum Algorithms

Quantum algorithms for solving a wide range of practical problems have been proposed in the last ten years, such as data search and analysis, product recommendation, and credit scoring. The concern about privacy and other ethical issues in quantum computing naturally rises up. In this paper, we define a formal framework for detecting violations of differential privacy for quantum algorithms. A detection algorithm is developed to verify whether a (noisy) quantum algorithm is differentially private and automatically generate bugging information when the violation of differential privacy is reported. The information consists of a pair of quantum states that violate the privacy, to illustrate the cause of the violation. Our algorithm is equipped with Tensor Networks, a highly efficient data structure, and executed both on TensorFlow Quantum and TorchQuantum which are the quantum extensions of famous machine learning platforms -- TensorFlow and PyTorch, respectively. The effectiveness and efficiency of our algorithm are confirmed by the experimental results of almost all types of quantum algorithms already implemented on realistic quantum computers, including quantum supremacy algorithms (beyond the capability of classical algorithms), quantum machine learning models, quantum approximate optimization algorithms, and variational quantum eigensolvers with up to 21 quantum bits

An innovative high accuracy autonomous navigation method for the Mars rovers

Autonomous navigation is an important function for a Mars rover to fulfill missions successfully. It is a critical technique to overcome the limitations of ground tracking and control traditionally used. This paper proposes an innovative method based on SINS (Strapdown Inertial Navigation System) with the aid of star sensors to accurately determine the rovers position and attitude. This method consists of two parts: the initial alignment and navigation. The alignment consists of a coarse position and attitude initial alignment approach and fine initial alignment approach. The coarse one is used to determine approximate position and attitude for the rover. This is followed by fine alignment to tune the approximate solution to accurate one. Upon the completion of initial alignment, the system can be used to provide real-time navigation solutions for the rover. An autonomous navigation algorithm is proposed to estimate and compensate the accumulated errors of SINS in real time. High accuracy attitude information from star sensor is used to correct errors in SINS. Simulation results demonstrate that the proposed methods can achieve a high precision autonomous navigation for Mars rovers. © 2014 IAA

Landau-Zener Tunnelling in a Nonlinear Three-level System

We present a comprehensive analysis of the Landau-Zener tunnelling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunnelling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunnelling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunnelling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunnelling probability when the nonlinear "internal field" resonate with the external field. We also discuss the asymmetry of the tunnelling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.Comment: 8 pages, 8 figure