Accelerating Quantum Tensor Network Simulations with Unified Path Variations and Non-Degenerate Batched Sampling

TL;DR

This paper introduces novel methods to significantly accelerate tensor network-based quantum simulations, achieving over 10^8 times speedup in data collection compared to traditional approaches.

Contribution

It develops error-independent path variation, non-degenerate sampling, and optimized contraction frameworks to vastly improve tensor network simulation efficiency.

Findings

Achieved over 10^8× data collection speedup with new methods.

Demonstrated more than 1000× speedup for general quantum simulations.

Enhanced tensor network sampling efficiency for noisy quantum system simulations.

Abstract

Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with $m$ stochastically sampled $2^n$-entry quantum statevectors rather than exact $2^{2n}$-entry density matrices. Recently, Pre-Trajectory Sampling with Batched Execution (PTSBE) has dramatically increased the data collection rate of these methods. While statevector PTSBE has demonstrated data collection speedups of over $10^6 \times$, tensor network implementations only achieved $\sim 15 \times$ speedup. This comparatively modest tensor network advantage stemmed from 1) contraction path recalculations, 2) sequential tensor network sampling, and 3) inflexible/unoptimized contraction hyperparameters. In this manuscript, we increase PTSBE's tensor network data collection rate to more than $10^8\times$ that of traditional trajectories methods by developing 1) error-independent unified path variation, 2) non-degenerate tensor network sampling, and 3) a flexible/optimized contraction framework. While our methods are particularly powerful for accelerating non-proportional sampling, we also demonstrate a more than $1000\times$ speedup for more general quantum simulations.