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arXiv:2406.08186 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Hiperwalk: Simulation of Quantum Walks with Heterogeneous High-Performance Computing

PAULO ROGERIO DA MOTTA JUNIOR, Gustavo A. Bezerra, Anderson Fernandes Pereira dos Santos, Renato Portugal

Published Sep 17, 2023• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1109/qce57702.2023.00055

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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.
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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.
Quantum walks provide a versatile framework for quantum algorithms across a wide range of applications. We develop efficient classical simulation methods for Szegedy quantum walks that avoid explicit construction of the full unitary evolution operator. Unlike previous approaches restricted to a particular walk formulation, our framework is built from fundamental update and reflection operators, enabling the simulation of a broader class of Szegedy walk formulations. We further extend these methods to phase-estimation-based algorithms coupled to the walk, including implementations suitable for large sparse graphs. The resulting methods achieve optimal O(N2)O(N^2)O(N2) complexity for dense graphs with NNN nodes. For sparse graphs, the computational cost scales linearly with the number of edges, which is O(N)O(N)O(N) in many cases. We implement the framework in the Python package SQWLib and illustrate its capabilities through simulations of representative algorithms, including quantum simulated annealing and quantum search on graphs. These results provide a practical tool for studying Szegedy-walk-based algorithms numerically beyond purely analytical treatments.
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.
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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.