IEEE Dallas Circuits and Systems Conference (DCAS)

Quantum SGD in Continuous-Time Limit by the Wigner Formulation of Open Quantum Systems

Avery Tovar, Brandon Lippe, José A. Morales Escalante

Published Apr 10, 2026• 0 citations

Abstract

This paper studies the continuous-time limit of a quantum analog of the classical Stochastic Gradient Descent (SGD) algorithm by formulating the problem in the Wigner description of quantum mechanics, thereby offering novelty in the description of the corresponding Stochastic Differential Equation (SDE) versus more obscure approaches regarding intuition, such as Lindblad formulations of quantum SGD algorithms. The Wigner formulation is a natural bridge between classical and quantum probabilistic algorithms, which, to our knowledge, has not been applied yet to the study of quantum analogs of SGD. We focus on the particular case of Quantum SGD in its continuous-time limit under a harmonic potential for the optimization of a quadratic function. We present both theoretical and computational studies of its convergence for the aforementioned benchmark problem. We prove, for this benchmark, the independence of the mixing time (convergence rate) from the phase-space dimension by studying the eigenvalues of the steadystate inverse covariance matrix in any dimension.

DOI: 10.1109/dcas69364.2026.11544686

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