Quantum walk, the quantum counterpart of random walk, is an important model and widely studied to develop new quantum algorithms. This paper studies the relationship between the continuous-time quantum walk and the symmetry of a graph, especially that of a tree. Firstly, we prove in mathematics that the symmetry of a graph is highly related to quantum walk. Secondly, we propose an algorithm based on the continuous-time quantum walk to compute the symmetry of a tree. Our algorithm has better time complexity O（N3） than the current best algorithm. Finally, through testing three types of 10024 trees, we find that the symmetry of a tree can be found with an extremely high efficiency with the help of the continuous-time quantum walk.
Nanocrossbar is a potential memory architecture to integrate memristor to achieve large scale and high density mem- ory. However, based on the currently widely-adopted parallel reading scheme, scalability of the nanocrossbar memory is limited, since the overhead of the reading circuits is in proportion with the size of the nanocrossbar component. In this paper, a multiplexed reading scheme is adopted as the foundation of the discussion. Through HSPICE simulation, we reanalyze scalability of the nanocrossbar memristor memory by investigating the impact of various circuit parameters on the output voltage swing as the memory scales to larger size. We find that multiplexed reading maintains sufficient noise margin in large size nanocrossbar memristor memory. In order to improve the scalability of the memory, memristors with nonlinear I-V characteristics and high LRS （low resistive state） resistance should be adopted.
Unipolar memristive devices are an important kind of resistive switching devices. However, few circuit models of them have been proposed. In this paper, we propose the SPICE modeling of flux-controlled unipolar memristive devices based on the memristance versus state map. Using our model, the flux thresholds, ON and OFF resistance, and compliance current can easily be set as model parameters. We simulate the model in HSPICE using model parameters abstracted from real devices, and the simulation results show that the proposed model caters to the real device data very well, thus demonstrating that the model is correct. Using the same modeling methodology, the SPICE model of charge-controlled unipolar memristive devices could also be developed. The proposed model could be used to model resistive memory cells, logical gates as well as synapses in artificial neural networks.
As the fourth passive circuit component, a memristor is a nonlinear resistor that can ＂remember＂ the amount of charge passing through it. The characteristic of ＂remembering＂ the charge and non-volatility makes memristors great potential candidates in many fields. Nowadays, only a few groups have the ability to fabricate memristors, and most researchers study them by theoretic analysis and simulation. In this paper, we first analyse the theoretical base and characteristics of memristors, then use a simulation program with integrated circuit emphasis as our tool to simulate the theoretical model of memristors and change the parameters in the model to see the influence of each parameter on the characteristics. Our work supplies researchers engaged in memristor-based circuits with advice on how to choose the proper parameters.
