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.
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.
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.
The Hiperwalk package is designed to facilitate the simulation of quantum walks using heterogeneous high-performance computing, taking advantage of the parallel processing power of diverse processors such as CPUs, GPUs, and acceleration cards. This package enables the simulation of both the continuous-time and discrete-time quantum walk models, effectively modeling the behavior of quantum systems on large graphs. Hiperwalk features a user-friendly Python package frontend with comprehensive documentation, as well as a high-performance C-based inner core that leverages parallel computing for efficient linear algebra calculations. This versatile tool empowers researchers to better understand quantum walk behavior, optimize implementation, and explore a wide range of potential applications, including spatial search algorithms.
Although many quantum algorithms have been developed in the last few decades with considerable speedup when compared to their best classical counterparts, the task of building a general purpose quantum computer is still a technological challenge. While the hardware necessary to run quantum algorithms is not available, researchers rely on classical simulations. However, the most interesting simulations are very demanding of computational resources due to the amount of data growing exponentially with the instance sizes and, thus, high performance computing techniques are necessary. Multiparticle quantum walks have been receiving a great deal of attention recently as a tool for designing quantum algorithms and for modeling physical phenomena. In the present work, we show that Apache Spark, a framework for large-scale data processing, can be used to simulate quantum walks with multiple interacting particles, with instance sizes that are impractical on single-processor, general-purpose computers. We also provide a prototype for quantum walks simulations, suitable to computer clusters, being developed atop of Spark.
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.
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.
Quantum computing is a developing field that applies the properties of quantum mechanics to develop solutions to complex problems that the most powerful classical computers cannot solve or cannot solve efficiently. Solving difficult tasks requires sophisticated and efficient algorithms that can utilize stochastic processes as the primary techniques. The typical models of these stochastic processes include discrete-time random walks and continuous ones. Quantum walks represent a quantum extension of discrete random walks, whose demonstrated utility in algorithm design has motivated signi cant interest in quantum computational research. Therefore, the purpose of this thesis is to explore the potential of discrete-time coined quantum walks using the Python package with high-performance computing (HPC) compared to classical walks by conducting a literature review. To supplement this research, some simulations are implemented to analyze the spreading behavior of coined quantum walks, compare them with classical walks, and demonstrate their application in search tasks, such as binary hypercube search algorithm. These simulations aim to clarify the extent to which quantum walks can be effectively modeled and applied in computational contexts. The results gained show that coined quantum walks exhibit faster spreading than classical random walks, which contributes to a deeper understanding of potential applications of quantum walks, such as quantum simulation, in the future.