Hamiltonian Simulation Using Nvidia CUDA-Q

Anurag Ramesh, W. Michael Brown, Thomas Lubinski, David E. Bernal Neira

Keywords: Hamiltonian simulation, CUDA-Q, GPU acceleration, Trotterization, multi-GPU scaling

Abstract:

Simulating quantum systems is a foundational application in quantum computing, especially in fields like computational chemistry
[1]. We present a scalable framework, the Quantum Economic Development Consortium (QED-C) Application-Oriented Benchmark Suite (https://github.com/SRI-International/QC-App-Oriented-Benchmarks)
to evaluate the performance of quantum algorithms across hardware platforms. A key focus is leveraging NVIDIA CUDA-Q [2], a powerful
GPU-accelerated platform for quantum-classical hybrid programming, to benchmark Hamiltonian simulation, Quantum Fourier Transform (QFT), and Phase Estimation (PE).
We simulate a range of physical systems within HamLib [3], includ ing the transverse field Ising, Heisenberg, and Fermi-Hubbard models,
as well as molecules such as H2 and B2 using Suzuki-Trotter evolution. Simulations were executed on NVIDIA GPU clusters, including
the A100, H100, GH200, and GB200 systems, across Purdue University [4], Lawrence Berkeley National Laboratory (LBNL) [5] and in collaboration with NVIDIA.
CUDA-Q’s SpinOperator formalism enabled emulation of circuits for up to 38 qubits on the LBNL cluster, with performance up to 3× faster than real quantum hardware. Strong scaling behavior is observed up to 32 GPUs, with execution times for some simulations
reduced by more than 90%. For example, execution times for simulating a 33-qubit TFIM dropped from 41 s (1 GPU) to 2.8 s (32 GPUs).
Despite these gains, we observe classical HPC-like diminishing returns beyond 8 GPUs, due to inter-GPU communication bottlenecks. This impact is mitigated on the latest GB200 clusters that support extending the high-bandwidth NVLink GPU interconnect across multiple nodes.
CUDA-Q proves especially effective for sampling-heavy workloads, offering near-linear scaling and improved parallel efficiency for PE and QFT as well.
Our findings demonstrate that GPU-accelerated quantum simulation with CUDA-Q provides a robust, high-throughput alternative
to noisy intermediate-scale quantum (NISQ) devices and paves the way for future kernel-level optimizations and distributed quantum computing strategies.

References:
1. Avimita Chatterjee, Sonny Rappaport, Anish Giri, Sonika Johri, Timothy Proctor, David E. Bernal Neira, Pratik Sathe, and Thomas Lubinski. A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations. 9 2024
2. NVIDIA. Cuda quantum. https://developer.nvidia.com/cuda-quantum, 2024
3. Sawaya, N.P.D., Marti-Dafcik, D., Ho, Y., Tabor, D.P., Bernal Neira, D.E., Magann, A.B., Premaratne, S., Dubey, P., Matsuura, A., Bishop, N., et al.: HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware. In: 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2, pp. 389–390. IEEE (2023)
4. G. McCartney, T. Hacker, and B. Yang, “Empowering Faculty: A Campus Cyber infrastructure Strategy for Research Communities,” Educause Review, 2014.
5. NERSC: Perlmutter (2022), https://www.nersc.gov/systems/perlmutter/

Submission Number: 1