Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time

TL;DR

This paper introduces an efficient algorithm converting pure bosonic Gaussian states into matrix product states, enabling scalable classical simulation of low-entanglement bosonic systems with significant speedups.

Contribution

The authors develop a novel method combining Gaussian SVD and a projected-creation-operator mapping to construct MPS without hafnian calculations, improving simulation efficiency.

Findings

Demonstrates speedups over previous tensor-network approaches on Gaussian boson sampling data.

Achieves target accuracy with manageable bond dimension in low-entanglement regimes.

Extends MPS applicability to a broader class of bosonic Gaussian states.

Abstract

Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step, however, is hindered by a significant bottleneck due to the hafnian. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), thereby establishing a versatile tool for probing bosonic Gaussian systems in settings where direct Gaussian-formalism-based calculations become inefficient. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement. In this regime, a target accuracy can be achieved with a bond dimension that remains computationally tractable, thereby extending the applicability of MPS-based methods to a broad range of bosonic systems.