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Computer Physics Communications

QWAK: Quantum walk analysis kit

Jaime Santos, Bruno Chagas, Rodrigo Chaves, Lorenzo Buffoni

Published May 21, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1016/j.cpc.2025.109676

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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 present qlbm , a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy tailored to the implementation of novel QBMs. The framework interfaces with state-of-the-art quantum software infrastructure to enable efficient simulation and validation pipelines, and leverages novel execution and pre-processing techniques that significantly reduce the computational resources required to develop quantum circuits. We demonstrate the versatility of the software by showcasing multiple QBMs in 2D and 3D with complex boundary conditions, integrated within automated benchmarking utilities. Accompanying the source code are extensive test suites, thorough online documentation resources, analysis tools, visualization methods, and demos that aim to increase the accessibility of QBMs while encouraging reproducibility and collaboration. Program summary Program Title: qlbm CPC Library link to program files: https://doi.org/10.17632/28hkvsg7p2.1 Developer's repository link: https://github.com/QCFD-Lab/qlbm Licensing provisions: MPL-2.0 Programming language: Python3 Supplementary material: The documentation of is available at https://qcfd-lab.github.io/qlbm/ . Nature of problem: The advent of quantum algorithms for computational fluid dynamics brings with it challenges that are new to the established field of computational physics. These challenges include the lack of standardized implementations of the still nascent quantum methods, the intense computational demands of developing and simulating quantum algorithms on hardware available today, and the absence of tools that integrate novel developments into established infrastructure. Because of these current limitations, physicists and mathematicians expend superfluous resources on tasks that more mature computational physics branches have surmounted long ago. Solution method: QLBM is a software package that provides an end-to-end development environment for quantum lattice Boltzmann methods. The modular design and flexible quantum circuit library provide a base for extending and generalizing quantum algorithms. Performance enhancements exploit the paradigm of quantum computing simulations to accelerate the speed at which researchers can verify the validity of their methods. Its integration with state-of-the-art quantum computing software and visualization tools increases the algorithms' accesibility. These features allow QLBM to effectively generate, simulate, and analyze quantum circuits for 2D and 3D computational fluid dynamics problems.
QuTiP, the Quantum Toolbox in Python (Johansson et al., 2012, Johansson et al., 2013), has been at the forefront of open-source quantum software for the past 13 years. It is used as a research, teaching, and industrial tool, and has been downloaded millions of times by users around the world. Here we introduce the latest developments in QuTiP v5, which are set to have a large impact on the future of QuTiP and enable it to be a modern, continuously developed and popular tool for another decade and more. We summarize the code design and fundamental data layer changes as well as efficiency improvements, new solvers, applications to quantum circuits with QuTiP-QIP, and new quantum control tools with QuTiP-QOC. Additional flexibility in the data layer underlying all “quantum objects” in QuTiP allows us to harness the power of state-of-the-art data formats and packages like JAX, CuPy, and more. We explain these new features with a series of both well-known and new examples. The code for these examples is available in a static form on GitHub ( https://github.com/qutip/qutip-paper-v5-examples ) and as continuously updated and documented notebooks in the qutip-tutorials package ( https://github.com/qutip/qutip-tutorials ).
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.
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.
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.
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with the Hamiltonian-driven time evolution of continuous walks. Through systematic analysis of probability distributions, standard deviations, and entanglement entropy on fundamental graph structures, we reveal distinctive dynamical characteristics that differentiate our model from conventional quantum walk paradigms. The proposed framework demonstrates unifying capabilities by naturally encompassing existing quantum walk models as special cases. Two significant applications emerge from this hybrid architecture: (1) We develop a novel protocol for perfect state transfer(PST) in general connected graphs, overcoming the limitations of previous graph-specific approaches. A PST on a tree graph has been implemented on a quantum superconducting processor. (2) We devise a quantum algorithm for multiplying K adjacency matrices of n -vertex regular graphs with time complexity O ( n 2 d 1 ⋯ d K ), outperforming classical matrix multiplication ( O ( n 2.371552 )) when vertex degrees d i are bounded. The algorithm’s efficacy for triangle counting is experimentally validated through the quantum simulation on PennyLane. These results establish the hybrid quantum walk as a versatile framework bridging discrete and continuous paradigms while enabling practical quantum advantage in graph computation tasks.