The QWalk Simulator of Quantum Walks

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.Comment: 21 pages, 11 figures. Accepted in Computer Physics Communications. Simulator can be downloaded from http://qubit.lncc.br/qwal

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Comment: 12 pages, 3 figures, see http://www.iitis.pl/~miszczak/trqs.html for related softwar

An efficient quantum circuit analyser on qubits and qudits

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates

QEDS: Um Simulador Clássico para Distinção de Elementos Quântico

 O problema de decidir se todos os N elementos em uma lista são distintos requer Omega(N) consultas no modelo clássico. Um algoritmo quântico baseado em caminhada quântica em um gráfico de Johnson melhora este limite para O(N2/3) consultas. O algoritmo quântico para a distinção de elementos executa vários cálculos, cada um envolvendo superposições não triviais de estados. Por esta razão, é difícil estudar o algoritmo sem ferramentas apropriadas. Neste trabalho, apresentamos um simulador numérico para o algoritmo de distinção de elementos e analisamos seu desempenho. O objetivo principal de nosso simulador é servir como uma ferramenta educacional. No entanto, como um software livre de código aberto, ele pode ser facimente estendido para uso profissional.

Symbolic quantum programming for supporting applications of quantum computing technologies

The goal of this paper is to deliver the overview of the current state of the art, to provide experience report on developing quantum software tools, and to outline the perspective for developing quantum programming tools supporting symbolic programming for the needs of quantum computing technologies. The main focus of this paper is on quantum computing technologies, as they can in the most direct way benefit from developing tools enabling the symbolic manipulation of quantum circuits and providing software tools for creating, optimizing, and testing quantum programs. We deliver a short survey of the most popular approaches in the field of quantum software development and we aim at pointing their strengths and weaknesses. This helps to formulate a list of desirable characteristics which should be included in quantum computing frameworks. Next, we describe a software architecture and its preliminary implementation supporting the development of quantum programs using symbolic approach, encouraging the functional programming paradigm, and, at the same, time enabling the integration with high-performance and cloud computing. The described software consists of several packages developed to address different needs, but nevertheless sharing common design concepts. We also outline how the presented approach could be used in tasks in quantum software engineering, namely quantum software testing and quantum circuit construction.Comment: 14 pages, contribution to QP2023 Workshop, Programming'23, Tokyo, JP, March 13-17, 202

SQUWALS: A Szegedy QUantum WALks Simulator

Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty of applications such as many variants of optimizations. In order to check its properties in an error-free environment, it is important to have a classical simulator. However, the current simulation algorithms require a great deal of memory due to the particular formulation of this quantum walk. In this paper we propose a memory-saving algorithm that scales as $\mathcal{O}(N^2)$ with the size $N$ of the graph. We provide additional procedures for simulating Szegedy's quantum walk over mixed states and also the Semiclassical Szegedy walk. With these techniques we have built a classical simulator in Python called SQUWALS. We show that our simulator scales as $\mathcal{O}(N^2)$ in both time and memory resources. This package provides some high-level applications for algorithms based on Szegedy's quantum walk, as for example the quantum PageRank.Comment: RevTex 4.2, 16 pages, 9 color figure

Quantum random walks: simulations and physical realizations

Dissertação de mestrado integrado em Engenharia FísicaQuantum computing is an emergent field that brings together Quantum Mechanics, Computer Science and Information Theory, which promises improvements to classical algorithms such as simulation of quantum systems, cryptography, data base searching and many others. Among these algorithms, quantum walks may provide a quadratic speed up when compared to their classical counterparts, allowing improvements to applications such as element distinctness, searching problems, matrix product verification and hitting times in graphs. The present work offers a general theoretical overview, simulation and circuit implementation of the coined, staggered and continuous-time quantum walk models. The first two chapters of this thesis are dedicated to the definition of the theoretical framework, simulation in Python and comparison of the aforementioned quantum walk models for the simple case of the dynamics in a line graph and for the search algorithm in a complete graph. This is then used as a benchmark for the final chapter, devoted to building and testing the circuits corresponding to models mentioned above in IBM’s Qiskit. A main contribution of this dissertation concerns the circulant graph approach to diagonal operators for continuous-time quantum walks.A computação quântica é uma área emergente, que junta os campos de Mecânica Quântica, Ciências da Computação e Teoria da Informação, com a promessa de melhoramentos a algoritmos clássicos tais como a simulação de sistemas quânticos, criptografia, busca em base de dados, e outros. Entre estes algoritmos, as caminhadas quânticas surgem com um ganho quadrático de complexidade em comparação às caminhadas clássicas, possibilitando melhor desempenho em aplicações como distinção de elementos, problemas de busca, verificação de produtos de matrizes e tempos de alcance em grafos. O trabalho atual oferece uma visão geral de um ponto de vista teórico, de simulação e de implementação de circuitos, relativos aos modelos de caminhadas quânticas com moeda, escalonadas e contínuas no tempo. Os primeiros dois capítulos desta tese são dedicados à definição da estrutura teórica, simulação em Python e comparação dos modelos supracitados, para o caso simples da dinâmica na linha, e para o problema de busca num grafo completo. Isto será então utilizado como referência para o capítulo final, dedicado à construção e teste dos circuitos correspondentes aos modelos supracitados. Uma contribuição principal desta dissertação diz respeito à abordagem de grafos circulantes para realização de caminhadas quânticas continuas no tempo.Finally, this dissertation was financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalization - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI- 01-0145-FEDER-030947

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

The QWalk simulator of quantum walks

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract 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 QWal... Title of program: QWalk Catalogue Id: AEAX_v1_0 Nature of problem Classical simulation of discrete quantum walks in one- and two-dimensional lattices. Versions of this program held in the CPC repository in Mendeley Data AEAX_v1_0; QWalk; 10.1016/j.cpc.2008.02.01