Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very important for the development of this area, since it allows the researchers to focus on the mathematical and physical aspects of the research instead of deviating the efforts to the implementation of specific numerical simulations. In this paper we present QWalk, a quantum walk simulator for one- and two-dimensional lattices. Finite two-dimensional lattices with generic topologies can be used. Decoherence can be simulated by performing measurements or by breaking links of the lattice. We use examples to explain the usage of the software and to show some recent results of the literature that are easily reproduced by the simulator.Program title: QWalkCatalogue identifier: AEAX_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenceNo. of lines in distributed program, including test data, etc.: 10 010No. of bytes in distributed program, including test data, etc.: 172 064Distribution format: tar.gzProgramming language: CComputer: Any computer with a C compiler that accepts ISO C99 complex arithmetic (recent versions of GCC, for instance). Pre-compiled Windows versions are also providedOperating system: The software should run in any operating system with a recent C compiler. Successful tests were performed in Linux and WindowsRAM: Less than 10 MB were required for a two-dimensional lattice of size 201×201. About 400 MB, for a two-dimensional lattice of size 1601×1601Classification: 16.5Nature of problem: Classical simulation of discrete quantum walks in one- and two-dimensional lattices.Solution method: Iterative approach without explicit representation of evolution operator.Restrictions: The available amount of RAM memory imposes a limit on the size of the simulations.Unusual features: The software provides an easy way of simulating decoherence through detectors or random broken links. In the two-dimensional simulations it also allows the definition of permanent broken links, besides calculation of total variation distance (from the uniform and from an approximate stationary distribution) and the choice between two different physical lattices. It also provides an easy way of performing measurements on specific sites of the 2D lattice and the analysis of observation screens. In one-dimensional simulations it allows the choice between three different lattices. Both one- and two-dimensional simulations facilitates the generation of graphics by automatically generating gnuplot scrips.Additional comments:•An earlier version of QWalk was first presented in [1].•The simulator generates gnuplot scripts that can be used to make graphics of the output data.•Several examples of input files are provided.Running time: The simulation of 100 steps for a two-dimensional lattice of size 201×201 took less than 2 seconds on a Pentium IV 2.6 GHz with 512 MB of RAM memory, 512 KB of cache memory and under Linux. It also took about 15 minutes for a lattice of size 1601×1601 on the same computer. Optimization option -O2 was used during compilation for these tests.References: [1] F.L. Marquezino, R. Portugal, QWalk: Simulador de caminhadas quânticas, in: Proceedings of 2nd WECIQ, Campina Grande, Brazil, IQuanta, 2007, pp. 123–132.
Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very important for the development of this area, since it allows the researchers to focus on the mathematical and physical aspects of the research instead of deviating the efforts to the implementation of specific numerical simulations. In this paper we present QWalk, a quantum walk simulator for one- and two-dimensional lattices. Finite two-dimensional lattices with generic topologies can be used. Decoherence can be simulated by performing measurements or by breaking links of the lattice. We use examples to explain the usage of the software and to show some recent results of the literature that are easily reproduced by the simulator.Program title: QWalkCatalogue identifier: AEAX_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEAX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenceNo. of lines in distributed program, including test data, etc.: 10 010No. of bytes in distributed program, including test data, etc.: 172 064Distribution format: tar.gzProgramming language: CComputer: Any computer with a C compiler that accepts ISO C99 complex arithmetic (recent versions of GCC, for instance). Pre-compiled Windows versions are also providedOperating system: The software should run in any operating system with a recent C compiler. Successful tests were performed in Linux and WindowsRAM: Less than 10 MB were required for a two-dimensional lattice of size 201×201. About 400 MB, for a two-dimensional lattice of size 1601×1601Classification: 16.5Nature of problem: Classical simulation of discrete quantum walks in one- and two-dimensional lattices.Solution method: Iterative approach without explicit representation of evolution operator.Restrictions: The available amount of RAM memory imposes a limit on the size of the simulations.Unusual features: The software provides an easy way of simulating decoherence through detectors or random broken links. In the two-dimensional simulations it also allows the definition of permanent broken links, besides calculation of total variation distance (from the uniform and from an approximate stationary distribution) and the choice between two different physical lattices. It also provides an easy way of performing measurements on specific sites of the 2D lattice and the analysis of observation screens. In one-dimensional simulations it allows the choice between three different lattices. Both one- and two-dimensional simulations facilitates the generation of graphics by automatically generating gnuplot scrips.Additional comments:•An earlier version of QWalk was first presented in [1].•The simulator generates gnuplot scripts that can be used to make graphics of the output data.•Several examples of input files are provided.Running time: The simulation of 100 steps for a two-dimensional lattice of size 201×201 took less than 2 seconds on a Pentium IV 2.6 GHz with 512 MB of RAM memory, 512 KB of cache memory and under Linux. It also took about 15 minutes for a lattice of size 1601×1601 on the same computer. Optimization option -O2 was used during compilation for these tests.References: [1] F.L. Marquezino, R. Portugal, QWalk: Simulador de caminhadas quânticas, in: Proceedings of 2nd WECIQ, Campina Grande, Brazil, IQuanta, 2007, pp. 123–132.
In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/ .
As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple graphical structure, exploitable symmetries, and case by case analyses. In more complex instances, as with most arbitrary graphs, the pursuit of a general solution is untenable. Enter Qwasi (Quantum Walk Simulator), a software tool that allows for the composition of arbitrary graphs by a user, includes a mathematical backend that can construct the Hilbert Space from these graphs, and simulates the evolution of the quantum walk as a set of numerical data. This simulation can be observed in real time, compiled into graphical plots, or exported as a CSV file. At present, the software focuses upon discrete-time scattering quantum walks, but expansion to other graph-based algorithms – anything that operates on a collection of vertices and connected edges – would not be a demanding task.
We describe software Quandoop, a novel simulator of discrete-time quantum walks using high-performance computing (HPC) with the goal of handling simulations with very large Hilbert spaces.Those simulations are usually restricted to a relatively small number of steps due to memory limitations or reduced processing power.The most important feature of Quandoop when compared to previous simulators is to provide a low cost solution for simulations of quantum walks with extreme memory requirements.Examples of such simulations include quantum walks on fractals or with multiple interacting walkers.Quandoop uses Apache Hadoop to parallelize the calculations on a computer cluster, thus reducing the amount of time required to perform the quantum walk simulation and allowing its execution with more steps.Our simulator takes the input as text files containing the initial state, the evolution operators and the description of simulation parameters.This approach allows the integration with other quantum walk simulators such as HiPerWalk or QWalk.After running the necessary calculations in parallel, Quandoop outputs text files describing the results associated to the quantum walk.
In this paper, we describe a continuous-time quantum walk (CTQW) simulation package for Python 3 , covering their theoretical foundations and practical applications. The software provides both unitary and open system evolution of over general graphs, alongside tools for visualization and exploration of several different aspects of the quantum walk. We go over installation, design and performance of the package, concluding with several examples on how QWAK can be used to explore problems such as search, perfect state transfer, among others. Additionally, we demonstrate how CuPy is utilized to leverage GPU acceleration. Program Summary/New Version Program Summary Program Title: QWAK CPC Library link to program files: https://doi.org/10.17632/wyrm54zc3f.1 Developer's repository link: https://github.com/JaimePSantos/QWAK Licensing provisions: CC By 4.0 Programming language: Python, Javascript, HTML and CSS. Nature of problem: QWAK simulates unitary and stochastic continuous-time quantum walks, focusing on transport property analysis, applications, visualization and ease of use. Solution method: We leverage Python 's vast package resources such as NumPy and NetworkX to implement the desired structures, and then generate the Hamiltonians via spectral decomposition. For the stochastic case, the Lindblad master equations are solved with Qutip . Additional comments including restrictions and unusual features: The GUI provided uses MongoDB to store QWAK objects, which currently limits the size of the graphs since the adjacency matrices are also stored.
We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk.
We describe program Hiperwalk, which is a new simulator of the main quantum walk models using high-performance computing (HPC).The simulator is able to generate the dynamics of discrete-time quantum walks and staggered quantum walks, and will be able simulate continuous-time quantum walks and Szegedy's quantum walks.It has an user-friendly input and is able to use hybrid HPC architectures, which includes the main ones available nowadays.The simulator outputs the main statistics associated with the probability distribution of the quantum walk in data files and automatically generates plots.The simulator uses open-source non-proprietary codes and employs freeware languages: Python, Neblina, Gnuplot, and OpenCL.