A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified geometric framework for adiabatic quantum mechanics.
Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this paradigm and discuss how to adopt it to the problem of binary clustering. Numerical …
Quantum computing speeds up linear regression training.
Quantum machine learning: Adiabatic quantum SVM outperforms classical methods.
This paper uses quantum computing to solve sparse linear regression problems efficiently.
We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree of the positive Hermitian …
Survey on quantum computing and neural networks.
New method uses adiabatic principles to improve ground-state preparation in quantum computing.
This paper uses QUBO to train machine learning models on quantum computers.
Quantum computing speeds up neural network training and retraining.
Quantum machine learns faster by reverse annealing on AQCs.
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…
Optimizes trading trajectories for large portfolios quickly.
Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which ta…
A key problem in financial mathematics is the forecasting of financial crashes: if we perturb asset prices, will financial institutions fail on a massive scale? This was recently shown to be a computationally intractable (NP-hard) problem. Financial crashes are inherently difficult to predict, even for a regulator whic…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped st…
Study topological quantum mechanics on orbifolds with geometric interpretation.
Quantum mechanics models for financial Black-Scholes model.
Examines quantum mechanics equivalence with Newtonian geometry.
Quantum-assisted VAE improves similarity search in high-dimensional datasets.
The paper studies distributions and controllability in quantum mechanical systems.
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
We present a simpler proof for the existence of adiabatic limits. Moreover, we added a new section where the adiabatic process is reversed and in some nondegenerate cases we deform the adiabatic limits to genuine irreducible solutions of the SW equations.
Study symmetry breaking in quantum mechanics to understand many-body physics.
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be…
The submanifold quantum mechanics was opened by Jensen and Koppe (Ann. Phys. {\bf 63} (1971) 586-591) and has been studied for these three decades. This article gives its more algebraic definition and show what is the essential of the submanifold quantum mechanics from an algebraic viewpoint.
New collapsing mechanism for G2-manifolds discovered.
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they are considered to share the same information content. The goal of tangle machine equivalence is to provide a context-independent me…
Study adiabatic limits of calibrated submanifolds in Riemannian geometry.
Quantum systems learn like machine learning models, influenced by dissipation.
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics …
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
Paper introduces a new deep-learning method for quantum mechanics.
We compare the covariant formulation of Quantum Mechanics on a curved spacetime fibred on absolute time with the standard Geometric Quantisation.
The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial market models are mapped by quantum mechanical ones.
The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.
The abstract discusses connecting quantum mechanics and algebraic index theories.
This text explains how fiber bundle structure is fundamental for classical physics.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on formulating different combinatorial optimization problems as Ising models, the core m…
We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
Study adiabatic limits of Calderon projector on manifolds with cylindrical ends.
New method uses quantum annealing and VAN for better statistical mechanics calculations.
We give an exposition, following joint works with J.-C. Zambrini, of the link between Euclidean Quantum Mechanics, Bernstein processes and isovectors for the heat equation. A new application to Mathematical Finance is then discussed.
Study asymptotics of unitary matrix elements in quantum mechanics.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…