Boundaries for quantum advantage with single photons and loop-based time-bin interferometers

TL;DR

This paper introduces an efficient classical simulation method for loop-based boson samplers, enabling better assessment of their potential for quantum advantage in time-bin interferometers.

Contribution

It presents a novel algorithm exploiting causal structures and a lattice path formalism to simulate loop-based boson sampling more efficiently than previous methods.

Findings

The new algorithm reduces classical simulation complexity for certain interferometer configurations.

A lattice path formalism characterizes the state space involved in simulations.

Heuristic estimates predict memory requirements, aiding in quantum advantage assessment.

Abstract

Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for demonstrating quantum advantage beyond the reach of classical emulation. We propose a method to exploit this loop-based structure to more efficiently classically sample from such systems. Our algorithm exploits a causal-cone argument to decompose the circuit into smaller effective components that can each be simulated sequentially by calling a state vector simulator as a subroutine. To quantify the complexity of our approach, we develop a new lattice path formalism that allows us to efficiently characterize the state space that must be tracked during the simulation. In addition, we develop a heuristic method that allows us to predict the expected average and worst-case memory requirements of running these simulations. We use these methods to compare the simulation complexity of different families of loop-based interferometers, allowing us to quantify the potential for quantum advantage of single-photon Boson Sampling in loop-based architectures.