Abstract
We present an approach for integrating the time evolution of quantum systems. We leverage the computation power of graphics processing units (GPUs) to perform the integration of all time steps in parallel. The performance boost is especially prominent for small to medium-sized quantum systems. The devised algorithm can largely be implemented using the recently-specified batched versions of the BLAS routines, and can therefore be easily ported to a variety of platforms. Our PARAllelized Matrix Exponentiation for Numerical Time evolution (PARAMENT) implementation runs on CUDA-enabled graphics processing units. Program summaryProgram Title: PARAMENTCPC Library link to program files:https://doi.org/10.17632/zy5v4xs89d.1Developer's repository link:https://github.com/parament-integrator/paramentLicensing provisions: Apache 2.0Programming language: C / CUDA / PythonNature of problem: Time-integration of the Schrödinger equation with a time-dependent Hamiltonian for quantum systems with a small Hilbert space but many time-steps.Solution method: A 4th order Magnus integrator, highly parallelized on a GPU, implemented using a small subset of BLAS functions for improved portability.
Highlights
The last decade has seen the advent of quantum technologies
We present an approach for integrating the time evolution of quantum systems
We present an approach for solving the time-dependent Schrödinger equation in a form that is frequently encountered in experimental realizations of a variety of physical quantum systems
Summary
The last decade has seen the advent of quantum technologies. Significant advances have paved the way for promising applications in computing, sensing or communication. Significant effort has been put on porting such simulations to GPUs. a lot of research focuses on small to mediumsized quantum systems. GHz control fields are applied for multiple microseconds leading to the need for integrating over tens of thousands of time steps. Often, this problem can be tackled by a suitable approximation (e.g. the rotating frame [1]). The implementation of matrix-matrix multiplication in suitable hardware structures, combined with fast memory access, allows for a fast and parallelized tackling of a variety of computational tasks. We present an approach for solving the time-dependent Schrödinger equation in a form that is frequently encountered in experimental realizations of a variety of physical quantum systems. We showcase the runtime and the convergence using a suitable example of a driven two-level system
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