Matrix product state approach to lossy boson sampling and noisy IQP sampling

TL;DR

This paper develops matrix product state algorithms to classically simulate noisy boson sampling and IQP sampling, revealing the boundary between quantum advantage and classical simulability in noisy quantum systems.

Contribution

It extends MPS-based classical simulation techniques to lossy boson sampling and noisy IQP models, improving control over accuracy and efficiency.

Findings

Classical simulability threshold at transmission rate O(1/√N)

Enhanced accuracy-efficiency trade-off in MPS algorithms

Broader applicability to noisy quantum sampling models

Abstract

Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them classically tractable. Motivated by the recent success of matrix product state (MPS)-based classical simulation of Gaussian boson sampling (Oh et al., 2024), we extend this framework to investigate the classical simulability of other noisy quantum sampling models. We develop MPS-based classical algorithms for lossy boson sampling and noisy instantaneous quantum polynomial-time (IQP) sampling, both of which retain the tunable accuracy characteristic of the MPS approach through the bond dimension. Our approach constructs pure-state decompositions of noisy or lossy input states whose components remain weakly entangled after circuit evolution, thereby providing a means to systematically explore the boundary between quantum-hard and classically-simulable regimes. For boson sampling, we analyze single-photon, Fock, and cat-state inputs, showing that classical simulability emerges at transmission rates scaling as $O(1/\sqrt{N})$, reaching the known boundary of quantum advantage with a tunable and scalable method. Beyond reproducing previous thresholds, our algorithm offers significantly improved control over the accuracy-efficiency trade-off. It further extends the applicability of MPS-based simulation to broader classes of noisy quantum sampling models, including IQP circuits.