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

• URL: http://arxiv.org/abs/2510.24137v2
• Date: Thu, 06 Nov 2025 01:36:47 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.

Related papers

• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Variational noise mitigation in quantum circuits: the case of Quantum Fourier Transform [35.18016233072556]
  We perform numerical simulations for two qubits under both coherent and incoherent noise.<n>Our results show that the variational circuit can reproduce the QFT with higher fidelity in scenarios dominated by coherent noise.<n>This demonstrates the potential of the approach as an effective error-mitigation strategy for small- to medium-scale quantum systems.
  arXiv  Detail & Related papers  (2025-11-07T14:35:55Z)
• Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits [1.9573380763700712]
  We propose an exact sampling algorithm that integrates tensor network contraction techniques with a Markov process.<n>As a demonstration, we target the challenge of generating samples from ideal and noisy QAOA circuits with up to 476 qubits.
  arXiv  Detail & Related papers  (2025-10-28T09:33:11Z)
• Classically Sampling Noisy Quantum Circuits in Quasi-Polynomial Time under Approximate Markovianity [0.616870773176256]
  We present a classical algorithm that runs in $nrmpolylog(n)$ time for simulating quantum circuits under local depolarizing noise.<n>Our results significantly extend the boundary of classical simulability and suggest that noise generically enforces approximate Markovianity and classical simulability.
  arXiv  Detail & Related papers  (2025-10-07T18:00:03Z)
• Classical Simulations of Low Magic Quantum Dynamics [0.1666604949258699]
  We develop algorithms for adaptive quantum circuits that produce states with low levels of magic.<n>These algorithms are particularly well-suited to circuits with high rates of Pauli measurements.<n>We study the dynamics of all-to-all monitored quantum circuits with a sub-extensive rate of T-gates per unit of circuit depth.
  arXiv  Detail & Related papers  (2025-08-27T20:17:15Z)
• A purely Quantum Generative Modeling through Unitary Scrambling and Collapse [6.647966634235082]
  Quantum Scrambling and Collapse Generative Model (QGen) is a purely quantum paradigm that eliminates classical dependencies.<n>We introduce a measurement-based training principle that decomposes learning into tractable subproblems, mitigating barren plateaus.<n> Empirically, QGen outperforms classical and hybrid baselines under matched parameter budget, while maintaining robustness under finite-shot sampling.
  arXiv  Detail & Related papers  (2025-06-12T11:00:21Z)
• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• Provably Robust Training of Quantum Circuit Classifiers Against Parameter Noise [49.97673761305336]
  Noise remains a major obstacle to achieving reliable quantum algorithms.<n>We present a provably noise-resilient training theory and algorithm to enhance the robustness of parameterized quantum circuit classifiers.
  arXiv  Detail & Related papers  (2025-05-24T02:51:34Z)
• Bayesian Quantum Amplitude Estimation [46.03321798937855]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Comparative Study of Sampling-Based Simulation Costs of Noisy Quantum Circuits [0.8206877486958002]
  We characterize the simulation costs of two major quantum schemes, stabilizer-state sampling of magic states and Heisenberg propagation. It revealed that in the low noise regime, stabilizer-state sampling results in a smaller sampling cost, while Heisenberg propagation is better in the high noise regime.
  arXiv  Detail & Related papers  (2020-11-12T07:12:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.