Efficient Quantum Circuit Simulation by Tensor Network Methods on Modern GPUs

Abstract

Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determines the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. Firstly, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Secondly, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96x reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5x compared to the state-of-the-art CPU-based results and 4.48-6.78x compared to the state-of-the-art GPU-based results reported in the literature.

25 pages, 10 figures

References in corpus (19)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Quantum computational advantage using photons
• A Quantum Approximate Optimization Algorithm
• Strong quantum computational advantage using a superconducting quantum processor
• Gaussian Boson Sampling
• Simulating quantum computation by contracting tensor networks
• NVIDIA Tensor Core Programmability, Performance & Precision
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Solving the sampling problem of the Sycamore quantum circuits
• Using Gaussian Boson Sampling to Find Dense Subgraphs
• Closing the "Quantum Supremacy" Gap: Achieving Real-Time Simulation of a Random Quantum Circuit Using a New Sunway Supercomputer
• A polynomial-time classical algorithm for noisy random circuit sampling
• Classical Simulation of Intermediate-Size Quantum Circuits
• Simulating Noisy Quantum Circuits with Matrix Product Density Operators
• Recovering single precision accuracy from Tensor Cores while surpassing the FP32 theoretical peak performance
• Classical Sampling of Random Quantum Circuits with Bounded Fidelity
• On Certified Randomness from Fourier Sampling or Random Circuit Sampling