Related papers: Quantum-Inspired Spectral Geometry for Neural Oper…
This paper proves quantum modularity of both functions from $\mathbb{Q}$ and $q$-series associated to the closed manifold obtained by $-\frac{1}{2}$ surgery on the figure-eight knot, $4_1(-1,2)$. In a sense, this is a companion to work of…
The natural gradient is central in neural quantum states optimizations but it is limited by the cost of computing and inverting the quantum geometric tensor, the quantum analogue of the Fisher information matrix. We introduce a…
Quantum State Tomography (QST) is essential for characterizing and validating quantum systems, but its practical use is severely limited by the exponential growth of the Hilbert space and the number of measurements required for…
Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…
Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite…
In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and…
We develop, as the first of a six-paper series, an operator-algebraic framework relating non-relativistic quantum mechanics and special relativity. Three structural facts organize the framework. (i)~The photon sector of free QED is a…
Exploring the potential of quantum hardware for enhancing classical and real-world applications is an ongoing challenge. This study evaluates the performance of quantum and quantum-inspired methods compared to classical models for crack…
Medical images are characterized by intricate and complex features, requiring interpretation by physicians with medical knowledge and experience. Classical neural networks can reduce the workload of physicians, but can only handle these…
Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. %and a potential building…
The main goal of this article is to study for a projective manifold and an ample line bundle over it the relation between metric and algebraic structures on the associated section ring. More precisely, we prove that once the kernel is…
Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…
Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…
We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex…
The bootstrap program for 1+1-dimensional integrable Quantum Field Theories (QFT's) is developed to a large extent for the Homogeneous sine-Gordon (HSG) models. This program can be divided into various steps, which include the computation…
Quantum Random Access Memory (QRAM) holds the promise of enabling several large scale applications of quantum computers. However, designing fault tolerant QRAMs for large scale applications is still an open problem due to the poor error and…
Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to…
Let $\mathcal{A}$ denote the operator class in which every nonzero intertwiner between two operators in $\mathcal{A}$ has dense range. Utilizing the operators in $\mathcal{A}$ as atoms and the flag structure as connection, we introduce an…
We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of…
The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum…