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

TL;DR

Hiperwalk tackles scalable quantum-walk simulation on graphs by marrying a user-friendly Python frontend with a high-performance C core that exploits heterogeneous HPC resources. It supports both continuous-time and coined quantum walks, implementing time evolution through $H = -\gamma A - \sum_{v\in M}|v\rangle\langle v|$ and $U(t)=e^{-iHt}$ for continuous-time, as well as $U=SC$ with a Grover coin for coined walks, enabling efficient state evolution and probability measurements. The paper details a layered architecture that decouples hardware-specific concerns via Neblina-inspired bridges and provides a Python wrapper API for dense and sparse linear algebra, accompanied by unit tests and multiple backends (OpenCL, CUDA, CPU). Preliminary results demonstrate comparable GPU performance and successful multi-bridge support, establishing a flexible, open-source platform for quantum-walk research, with applications to quantum algorithms and spatial search on large graphs.

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.

Figures (6)

• Figure 1: Excerpt from a Jupyter Notebook showing the commands that plot the probability distribution of a continuous-time quantum walk at $t=50$.
• Figure 2: Excerpt from a Jupyter Notebook showing the commands that plot the probability distribution of a coined quantum walk on a two-dimensional grid.
• Figure 3: Neblina Core model.
• Figure 4: A Python program that uses the Neblina API.
• Figure 5: Python code for vector-matrix multiplication.