Quantum Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems

2025/10/29 by Escalante, Jose A. Morales
#Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2510.25910

Abstract

The main ideas behind a research plan to use the Wigner formulation as a bridge between classical and quantum probabilistic algorithms are presented, focusing on a particular case: the Quantum analog of Stochastic Gradient Descent in its continuous-time limit based on the Wigner formulation of Open Quantum Systems.

Citations

• On the Validity of Modeling SGD with Stochastic Differential Equations (SDEs)
• On Learning Rates and Schrödinger Operators
• Understanding the Acceleration Phenomenon via High-Resolution Differential Equations
• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• The Wigner-Fokker-Planck equation: Stationary states and large-time\n behavior
• On the Long Time Behavior of the Quantum Fokker-Planck equation

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