Adaptive Tensor Network Simulation via Entropy-Feedback PID Control and GPU-Accelerated SVD
This work addresses computational inefficiency in quantum many-body simulations for researchers, offering incremental improvements in adaptive resource allocation.
The paper tackles the challenge of selecting bond dimension in tensor network simulations by introducing an adaptive framework using entropy feedback and PID control, achieving a 2.7x reduction in wall time and energy accuracy within 0.1% of exact solutions.
Tensor network methods, particularly those based on Matrix Product States (MPS), provide a powerful framework for simulating quantum many-body systems. A persistent computational challenge in these methods is the selection of the bond dimension chi, which controls the trade-off between accuracy and computational cost. Fixed bond dimension strategies either waste resources in low-entanglement regions or lose fidelity in high-entanglement regions. This work introduces an adaptive bond dimension management framework that uses von Neumann entropy feedback coupled with a Proportional-Integral-Derivative (PID) controller to dynamically adjust chi at each bond during simulation. An Exponential Moving Average (EMA) filter stabilizes entropy measurements against transient fluctuations, and a predictive scheduling module anticipates future bond dimension requirements from entropy trends. The per-bond granularity of the allocation ensures that computational resources concentrate where entanglement is largest. The framework integrates GPU-accelerated Singular Value Decomposition (SVD) via CuPy and the cuSOLVER backend, achieving individual SVD speedups of 4.1x at chi=256 and 7.1x at chi=2048 relative to CPU-based NumPy for isolated matrix factorisations (measured on an NVIDIA A100-SXM4-40GB GPU with CuPy 13.4.1 and CUDA 12.8). At the system level, benchmarks on the spin-1/2 antiferromagnetic Heisenberg chain demonstrate a 2.7x reduction in total DMRG wall time compared to fixed-chi simulations, with energy accuracy within 0.1% of the Bethe ansatz solution. Integration with the Density Matrix Renormalization Group (DMRG) algorithm yields ground-state energies per site converging to E/N = -0.4432 for the isotropic Heisenberg model at chi = 128. Validation against Amazon Web Services (AWS) Braket SV1 statevector simulator confirms agreement within 2-5% for small systems.