Control of Overfitting with Physics.

While there are many works on the applications of machine learning, not so many of them are trying to understand the theoretical justifications to explain their efficiency. In this work, overfitting control (or generalization property) in machine learning is explained using analogies from physics and biology. For stochastic gradient Langevin dynamics, we show that the Eyring formula of kinetic theory allows to control overfitting in the algorithmic stability approach-when wide minima of the risk function with low free energy correspond to low overfitting.

Correction: Morzhin, O.V.; Pechen, A.N. Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives. 2024, , 36.

In the published article [...

Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives.

This article is devoted to developing an approach for manipulating the von Neumann entropy S(ρ(t)) of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy S(ρ(T)); (b) steering S(ρ(T)) to a given target value; (c) steering S(ρ(T)) to a target value and satisfying the pointwise state constraint S(ρ(t))≤S¯ for a given S¯; (d) keeping S(ρ(t)) constant at a given time interval. Under the Markovian dynamics determined by a Gorini-Kossakowski-Sudarshan-Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals.

Uncomputability and complexity of quantum control.

In laboratory and numerical experiments, physical quantities are known with a finite precision and described by rational numbers. Based on this, we deduce that quantum control problems both for open and closed systems are in general not algorithmically solvable, i.e.

Are there traps in quantum control landscapes?

There has been great interest in recent years in quantum control landscapes. Given an objective J that depends on a control field ε the dynamical landscape is defined by the properties of the Hessian δ²J/δε² at the critical points δJ/δε=0. We show that contrary to recent claims in the literature the dynamical control landscape can exhibit trapping behavior due to the existence of special critical points and illustrate this finding with an example of a 3-level Λ system.