Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM, with a focus on the effect of the unit priors on learning efficiency. We consider a parametric class of priors that interpolate between continuous (Gaussian) and binary variables. This approach models various possible choices of visible units, hidden units, and weights for both the teacher and student RBMs. By analyzing the phase diagram of the posterior distribution in both the Bayes optimal and mismatched regimes, we demonstrate the existence of a triple point that defines the critical dataset size necessary for learning through generalization. The critical size is strongly influenced by the properties of the teacher, and thus the data, but is unaffected by the properties of the student RBM. Nevertheless, a prudent choice of student priors can facilitate training by expanding the so-called signal retrieval region, where the machine generalizes effectively.

This study presents a machine-learning-based procedure to automate the charge tuning of semiconductor spin qubits with minimal human intervention, addressing one of the significant challenges in scaling up quantum dot technologies. This method exploits artificial neural networks to identify noisy transition lines in stability diagrams, guiding a robust exploration strategy leveraging neural networks' uncertainty estimations. Tested across three distinct offline experimental datasets representing different single quantum dot technologies, the approach achieves over 99% tuning success rate in optimal cases, where more than 10% of the success is directly attributable to uncertainty exploitation. The challenging constraints of small training sets containing high diagram-to-diagram variability allowed us to evaluate the capabilities and limits of the proposed procedure.

The appendix is subdivided into the following seven topics: A Central angle property: Quick proof of the central angle property, used in Sect. B Optimal Land V-shaped branching: Derivation of the conditions listed in Tab. 1 under which V-or L-branching are optimal. E Non-optimality of higher-degree branchings: Technical proofs and numerical scheme to show the non-optimality of higher-degree branchings discussed in Sect. F BOT on two-dimensional Riemannian manifolds: Formal proof of Theorem 5.1, which generalizes the optimal branching conditions and other properties from the Euclidean plane to embedded surfaces. A sketch of the proof can be found in Sect. G Algorithms: Additional details and experiments for the different algorithms presented in the main paper. Section G.2 focuses on the numerical geometry optimization and Sect. Section G.1 holds a few examples of the recursive geometric construction of relatively optimal solutions for BOT problems with multiple sources. In this section, we present a geometric proof of the central angle property used in the geometric construction of relatively optimal solutions for a given full tree topology (see Sect. 3.2). Below, we formally derive the conditions listed in Tab. 1 under which V-or L-branching provide the optimal solution to a BOT problem with one source and two sinks.

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route, favoring branched transportation networks. We here study the NP-hard optimization of BOT networks connecting a finite number of sources and sinks in $\mathbb{R}^2$. First, we show how to efficiently find the best geometry of a BOT network for many sources and sinks, given a topology. Second, we argue that a topology with more than three edges meeting at a branching point is never optimal. Third, we show that the results obtained for the Euclidean plane generalize directly to optimal transportation networks on two-dimensional Riemannian manifolds. Finally, we present a simple but effective approximate BOT solver combining geometric optimization with a combinatorial optimization of the network topology.

We present exact analytical equilibrium solutions for a class of recurrent neural network models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour and long-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.

We present exact analytical equilibrium solutions for a class of recurrent neural network models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour and long-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.

We present exact analytical equilibrium solutions for a class of recurrent neuralnetwork models, with both sequential and parallel neuronal dynamics, in which there is a tunable competition between nearestneighbour andlong-range synaptic interactions. This competition is found to induce novel coexistence phenomena as well as discontinuous transitions between pattern recall states, 2-cycles and non-recall states.