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

• URL: http://arxiv.org/abs/2510.24137v1
• Date: Tue, 28 Oct 2025 07:23:10 GMT
• Title: Matrix product state approach to lossy boson sampling and noisy IQP sampling
• Authors: Sojeong Park, Changhun Oh,
• Abstract summary: We develop classical algorithms for lossy boson sampling and noisy instantaneous quantum-time sampling.<n>Our algorithm offers significantly improved control over the accuracy-efficiency trade-off.<n>It further extends the applicability of MPS simulation to broader classes of noisy quantum sampling models.
• Score: 0.7066293026438526
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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