Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems

2026-04-21

AI Summary

This work addresses bosonic quantum systems with Kerr nonlinearity—central to universal bosonic quantum computation and driven Bose-Hubbard models—and proposes a Schrödinger-picture simulation method based on sparse superpositions of coherent states. By introducing an error-controlled truncation scheme and approximation mechanism, the approach substantially reduces computational complexity under conditions of weak nonlinearity or a limited number of Kerr gates. The study establishes the first scalable classical simulation framework, demonstrating quasi-polynomial-time simulability for logarithmically many Kerr gates and delineating a polynomial-time simulable regime in the weak-nonlinearity limit. Numerical experiments on fully connected Bose-Hubbard models reproduce benchmark results obtained with Fock-state and matrix product state methods, confirming the method’s validity and practical potential.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum computation that is also physically motivated by driven Bose-Hubbard dynamics. The method works in the Schrödinger picture representing the evolving state as a sparse superposition of coherent states. We develop approximation strategies that keep the simulation cost tractable in physically relevant regimes, notably when the number of Kerr gates is small or the Kerr nonlinearities are weak, and prove rigorous guarantees for both observable estimation and sampling. In particular, bosonic circuits with logarithmically many Kerr gates admit quasi-polynomial-time classical simulation at exponentially small error in trace distance. We further identify a weak-nonlinearity regime in which the runtime is polynomial for arbitrarily small constant precision. We complement these results with numerical benchmarks on the Bose-Hubbard model with all-to-all connectivity. The method reproduces Fock-basis and matrix-product-state reference data, suggesting that it offers a useful route to the classical simulation of bosonic systems.

Problem

• bosonic quantum systems
• Kerr nonlinearity
• classical simulation
• coherent states
• Bose-Hubbard model

Innovation

• coherent-state propagation
• bosonic quantum simulation
• Kerr nonlinearity
• classical simulability
• sparse coherent-state representation