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Computer Physics Communications

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

Josh Izaac, Jingbo B. Wang

Published Sep 22, 2014• 25 citations
Publisher
DOI
10.1016/j.cpc.2014.09.011

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The continuous-time quantum walk (CTQW) is the quantum analogue of the continuous-time classical walk and is widely used in universal quantum computations. Here, taking the advantages of the waveguide arrays, we implement large-scale CTQWs on chips. We couple the single-photon source into the middle port of the waveguide arrays and measure the emergent photon number distributions by utilizing the fiber coupling platform. Subsequently, we simulate the photon number distributions of the waveguide arrays by considering the boundary conditions. The boundary conditions are quite necessary in solving the problems of quantum mazes.
Quantum walks are a fundamental tool in the study of quantum information, bridging the gap between quantum computation and modelling complex systems. In this thesis, we present a software package for simulation of multiparticle continuous-time quantum walks (CTQWs) using high performance computation, and detail a method of systematic dimensionalty reduction for fermionic CTQWs. We then consider CTQW applications; proving that the single particle CTQW is unsuited for determining graph isomorphism, and proposing a CTQW-based network centrality algorithm. This algorithm is utilized in the first successful physical quantum centrality implementation. Finally, we extend our centrality algorithm to PT-symmetric directed graphs.
The proposed quantum hash function (QHF) based on the discrete-time quantum walk (DTQW) structure requires enlarging the coin state space and the preparation of continuous quantum states is less difficult. Hence, a new construction method of QHF is proposed based on the continuous-time quantum walk (CTQW) of the one-dimensional (1D) lattice with boundary constraints and without additional coin space. In the scheme, the input of the QHF is an arbitrary binary string message which is used to control the selected Hamiltonian of CTQW at each time interval, and the output of the QHF is the final probability distribution of CTQW. Under the same computing environment, simulation and analysis indicate that our QHF can satisfy the same security requirements such as sensitivity, diffusion and confusion, collision, birthday attack, but the collision rate is reduced by 40% without reducing effectiveness.