GPU-accelerated Effective Hamiltonian Calculator

TL;DR

This paper introduces GPU-accelerated numerical techniques inspired by NPAD and Magnus expansion for efficient effective Hamiltonian calculations in large quantum systems, demonstrated in circuit-QED models and available as open-source software.

Contribution

The authors develop and provide GPU-accelerated numerical methods based on NPAD and Magnus expansion, optimized for large quantum systems, with open-source implementation.

Findings

Up to 15x GPU speedup for NPAD

Up to 42x GPU speedup for Magnus expansion

Effective Hamiltonian calculations for large quantum systems

Abstract

Effective Hamiltonian calculations for large quantum systems can be both analytically intractable and numerically expensive using standard techniques. In this manuscript, we present numerical techniques inspired by Nonperturbative Analytical Diagonalization (NPAD) and the Magnus expansion for the efficient calculation of effective Hamiltonians. While these tools are appropriate for a wide array of applications, we here demonstrate their utility for models that can be realized in circuit-QED settings. Our numerical techniques are available as an open-source Python package, ${\rm qCH_{eff}}$, which is available on GitHub (https://github.com/NVlabs/qCHeff) and PyPI (https://pypi.org/project/qcheff/). We use the CuPy library for GPU-acceleration and report up to 15x speedup on GPU over CPU for NPAD, and up to 42x speedup for the Magnus expansion (compared to QuTiP), for large system sizes.