Graphon Quantum Filtering Systems

2025/06/13 by Hamed Amini, Nina H. Amini, Amini, Hamed +5 · 1 citation
Computer Science · Materials Science · #49N80 #60H30 #60K35 #81S22 #81S25 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Graphene research and applications #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2506.12249

openalex publication_date 2025/06/13 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We consider a non-exchangeable system of interacting quantum particles with mean-field type interactions, subject to continuous measurement on dense graphs. In the mean-field limit, we derive a graphon-based quantum filtering system, establish its well-posedness, and prove propagation of chaos for multi-class bosonic systems with blockwise interactions. We then discuss applications to quantum state preparation and quantum graphon games.

Citations

• Brownian motion on the Fubini extension space and applications
• On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States
• Quantum model reduction for continuous-time quantum filters
• Interacting particle systems on sparse W-random graphs
• On quantum Stochastic Master equations
• Nonlinear Graphon mean-field systems
• Large-population limits of non-exchangeable particle systems
• Exponential Selection and Feedback Stabilization of Invariant Subspaces of Quantum Trajectories
• Stochastic Graphon Games with Jumps and Approximate Nash Equilibria
• On the mean-field Belavkin filtering equation
• A label-state formulation of stochastic graphon games and approximate equilibria on large networks
• Pickl's Proof of the Quantum Mean-Field Limit and Quantum Klimontovich Solutions
• Mean-field limit of non-exchangeable systems
• Stochastic Graphon Games: II. The Linear-Quadratic Case
• Quantum mean field games
• Graphon mean field systems
• Graphon mean field systems
• On exponential stabilization of N-level quantum angular momentum systems
• Continuous-time Quantum Error Correction with Noise-assisted Quantum\n Feedback
• Stochastic integration in Banach spaces - a survey
• Derivation of Hartree's theory for generic mean-field Bose systems
• Kac's Program in Kinetic Theory
• A simple derivation of mean field limits for quantum systems
• Individual Risk and Lebesgue Extension without Aggregate Uncertainty
• Hamilton–Jacobi–Bellman equations for quantum optimal feedback control
• Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate
• Deterministic Dicke state preparation with continuous measurement and control
• The law of large numbers with a continuum of IID random variables
• The exact law of large numbers via Fubini extension and characterization of insurable risks

Cited by

• Brownian motion on the Fubini extension space and applications

Related

• Quantum mean field games
• On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States
• Bosonic Random Walk Networks for Graph Learning
• Quantum Filtering for Systems Driven by Fields in Single Photon States and Superposition of Coherent States using Non-Markovian Embeddings
• Quantum filtering for systems driven by fermion fields