Related papers: Circuit theory in projective space and homogeneous…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
In this paper we address the problem of translating one-way quantum computation (1WQC) into the circuit model. We start by giving a straightforward circuit representation of any 1WQC, at the cost of introducing many ancilla wires. We then…
Quantum computers can efficiently sample from probability distributions that are believed to be classically intractable, providing a foundation for quantum generative modeling. However, practical training of such models remains challenging,…
Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to…
When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…
We present a theoretical and a numerical formalism for analysis and design of spintronic integrated circuits (SPINICs). The formalism encompasses a generalized circuit theory for spintronic integrated circuits based on nanomagnetic dynamics…
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or projective geometry. We show that the two smallest projective…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…
We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and…
Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an…
Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture…
Circuits play a fundamental role in polyhedral theory and linear programming. For instance, circuits are used as step directions in various augmentation schemes for solving linear programs or to leave degenerate vertices while running the…
An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…
Variational quantum algorithms, inspired by neural networks, have become a novel approach in quantum computing. However, designing efficient parameterized quantum circuits remains a challenge. Quantum architecture search tackles this by…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
Recently Bravyi, Gosset and K\"onig (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…