Quantum walk on a vibrating lattice and its numerical study with a GPU-accelerated algorithm

Enrico Piccinini, Claudia Benedetti, Ilaria Siloi +2 more

Marek Sawerwain, Roman Gielerak

José M. Rodríguez-Borbón, Xian Wang, Adrián Perez Diéguez +2 more

We present an open-source software package, TRAVOLTA (Terrific Refinements to Accelerate, Validate, and Optimize Large Time-dependent Algorithms), for carrying out massively parallelized quantum optimal control calculations on GPUs. The TRAVOLTA software package is a significant overhaul of our previous NIC-CAGE algorithm and also includes algorithmic improvements to the gradient ascent procedure to enable faster convergence. We examine three different variants of GPU parallelization to assess their performance in constructing optimal control fields in a variety of quantum systems. In addition, we provide several examples with extensive benchmarks on our GPU-enhanced TRAVOLTA code to show that it generates the same results as previous CPU-based algorithms but with a speedup that is more than ten times faster. Our GPU enhancements and algorithmic improvements enable large quantum optimal control calculations that can be efficiently and routinely executed on modern multi-core computational hardware. Program Title: TRAVOLTA CPC Library link to program files: https://doi.org/10.17632/grwppm37rn.1 Licensing provisions: GNU General Public License 3 Programming language: C++ and CUDA Supplementary material: Brief review of LU decomposition and raw numerical values used to generate Fig. 6 in the main text. Nature of problem: The TRAVOLTA software package utilizes GPU accelerated routines and new algorithmic improvements to compute optimized electric fields that can drive a system from a known initial vibrational eigenstate to a specified final quantum state with a large (≈1) transition probability. Solution method: Quantum control, GPU acceleration, analytic gradients, Crank-Nicolson propagation, and gradient ascent optimization.

Yen-Jui Chang, Weiting Wang, Chen-Yu Liu +2 more

Abstract We present a novel Adaptive Distribution Generator (ADG) that leverages a quantum walks–based approach to generate high precision and efficiency of target probability distributions. Our method integrates variational quantum circuits with discrete-time quantum walks(DTQWs)—specifically, split-step quantum walks(SSQWs) and their entangled extensions—to dynamically tune coin parameters and drive the evolution of quantum states toward desired distributions. This enables accurate one-dimensional probability modeling for applications such as financial simulation and the generation of structured two-dimensional patterns, exemplified by digit representations (0–9). Implemented within the CUDA-Q framework, our approach exploits GPU acceleration to significantly reduce computational overhead and improve scalability relative to conventional methods. Extensive benchmarks demonstrate that our Quantum Walk–Based Adaptive Distribution Generator (QWs-based ADG) achieves high simulation fidelity and bridges the gap between theoretical quantum algorithms and practical high-performance computation.

Tirthaprasad Chattaraj, Roman V. Krems

Asif Shakeel