Efficient construction of tensor-network representations of many-body Gaussian states

TL;DR

This paper introduces an efficient method to construct tensor-network representations of many-body Gaussian states, significantly reducing computational time and enabling advanced simulations of quantum many-body systems.

Contribution

It presents a novel procedure that combines Gaussian quantum information theory with tensor-network methods to efficiently represent and simulate many-body Gaussian states.

Findings

Reduces construction time by up to five orders of magnitude.

Enables simulations of larger quantum systems beyond previous capabilities.

Provides a controllable error in tensor-network representations.

Abstract

We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems. The procedure improves computational time requirements for constructing many-body Gaussian states by up to five orders of magnitude for reasonable parameter values, thus allowing simulations beyond the range of what was hitherto feasible. Our procedure combines ideas from the theory of Gaussian quantum information with tensor-network based numerical methods thereby opening the possibility of exploiting the rich tool-kit of Gaussian methods in tensor-network simulations.