Simulating Gaussian Boson Sampling with Tensor Networks in the Heisenberg picture

TL;DR

This paper introduces a tensor network method in the Heisenberg picture for simulating Gaussian boson sampling, improving efficiency and enabling realistic loss modeling, thus advancing quantum computing simulations.

Contribution

The paper presents a novel tensor network approach in the Heisenberg picture for Gaussian boson sampling, enhancing simulation capabilities and handling non-uniform photon losses.

Findings

Efficient simulation of Gaussian boson sampling using tensor networks in the Heisenberg picture.

Ability to simulate realistic setups with non-uniform photon losses.

Demonstrated potential to improve quantum computing research through better simulation methods.

Abstract

Although the Schr{\"o}dinger and Heisenberg pictures are equivalent formulations of quantum mechanics, simulations performed choosing one over the other can greatly impact the computational resources required to solve a problem. Here we demonstrate that in Gaussian boson sampling, a central problem in quantum computing, a good choice of representation can shift the boundary between feasible and infeasible numerical simulability. To achieve this, we introduce a novel method for computing the probability distribution of boson sampling based on the time evolution of tensor networks in the Heisenberg picture. In addition, we overcome limitations of existing methods enabling simulations of realistic setups affected by non-uniform photon losses. Our results demonstrate the effectiveness of the method and its potential to advance quantum computing research.