Classical simulation of lossy boson sampling using matrix product operators

TL;DR

This paper investigates the classical simulability of lossy boson sampling on NISQ devices using matrix product operators, revealing how photon loss impacts computational complexity and simulation efficiency.

Contribution

It introduces an MPO-based simulation approach for lossy boson sampling and analyzes how photon loss affects classical simulation complexity.

Findings

MPO simulation accuracy can be efficiently controlled by bond dimension.

Simulation complexity depends on the scaling of input and output photon numbers.

Exponential time complexity arises when output photons grow faster than the square root of input photons.

Abstract

Characterizing the computational advantage from noisy intermediate-scale quantum (NISQ) devices is an important task from theoretical and practical perspectives. Here, we numerically investigate the computational power of NISQ devices focusing on boson sampling, one of the well-known promising problems which can exhibit quantum supremacy. We study hardness of lossy boson sampling using matrix product operator (MPO) simulation to address the effect of photon-loss on classical simulability using MPO entanglement entropy (EE), which characterizes a running time of an MPO algorithm. An advantage of MPO simulation over other classical algorithms proposed to date is that its simulation accuracy can be efficiently controlled by increasing an MPO's bond dimension. Notably, we show by simulating lossy boson sampling using an MPO that as an input photon number grows, its computational cost, or MPO EE, behaves differently depending on a loss-scaling, exhibiting a different feature from that of lossless boson sampling. Especially when an output photon number scales faster than the square root of an input photon number, our study shows an exponential scaling of time complexity for MPO simulation. On the contrary, when an output photon number scales slower than the square root of an input photon number, MPO EE may decrease, indicating that an exponential time complexity might not be necessary.