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.
A reinforcement learning approach prepares quantum squeezed states in open spin systems.
Generative neural samplers estimate quantum spin system properties.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
Spin-opstrings from QMC simulations enable ML of quantum phases.
New pseudo-Hermitian models from non-semisimple TQFTs.
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the standard technique for mapping the quantum spin systems to the classical ones. In this…
Quantum systems on coadjoint orbits yield spectra matching Dolbeault and de Rham indices.
Efficiently predicts long-time dynamics of quantum spin models using MLP regression.
Quantum map counts BPS states in special theories.
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
The abstract discusses financial irreversibility using quantum mechanics and projective geometry.
The tail of a quantum spin network in the two-sphere is a -series associated to the network. We study the existence of the head and tail functions of quantum spin networks colored by . We compute the -series for an infinite family of quantum spin networks and give the relation between the tail of these networ…
New spin on Khovanov-Rozansky homology categorifies spin link polynomial.
Spin networks boost quantum algorithms solving SU(2) symmetric problems.
Machine learning classifies phases of spin models using improved correlation configurations.
We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley-Lieb algebra) does not support a chiral conformal field theory whose Hamiltonian generates translation on the circle as a continuous limit of the rotations on the lattice.
Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or generalized spin and complex spin structures. A crucial role in our construction is play…
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
In a previous paper we constructed classical spin Chern-Simons for any compact Lie group : a gauge theory whose action depends on the spin structure of the 3-manifold. Here we apply geometric quantization to the classical Hamiltonian theory and investigate the formal properties of the partition function in the Lagra…
Covariant formulation of Barbero-Immirzi connections for spin manifolds.
The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes whose graded Euler characteristic is the "classical" projector in the Temperley-Lieb algebra. We show that they are homotopy…
Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifol…
A spin network is a cubic ribbon graph labeled by representations of . Spin networks are important in various areas of Mathematics (3-dimensional Quantum Topology), Physics (Angular Momentum, Classical and Quantum Gravity) and Chemistry (Atomic Spectroscopy). The evaluation of a spin network is an integ…
Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter is a root of unity of order where is odd or congruent to modulo . In this paper we consider…
The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fi…
Quantum reservoir computing needs coherence influx for effective information processing.
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin group. The differential operators can be seen as a generalization to higher spin …
Quantum strategy optimizes wealth growth in a double-or-nothing game.
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural backgraund, we would like to change the tack: to relate discrete (combinatorial) objects …
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in open systems and its absence in closed ones, we prove sharp, state-independent i…
New quantum integrals discovered for a spin chain model.
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…
Study classifies moduli spaces of spin connections on 3D homogeneous spaces.
A classical spin network consists of a ribbon graph (i.e., an abstract graph with a cyclic ordering of the vertices around each edge) and an admissible coloring of its edges by natural numbers. The standard evaluation of a spin network is an integer number. In a previous paper, we proved an existence theorem for the as…
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of Restricted Boltzmann Machines and some classes of Tensor-Network states in arbitrary dime…
Study quantum diffusion on spectral triples and spinor bundles.
We introduce the stack of r-spin maps. These are stable maps into a variety V from n-pointed algebraic curves of genus g, with the additional data of an r-spin structure on the curve. We prove that this stack is a Deligne-Mumford stack, and we define analogs of the Gromov-Witten classes associated to these spaces. We s…
An elementary family of local Hamiltonians , is described for a dimensional quantum mechanical system of spin particles. On the torus, the ground state space is extensively degenerate but should collapse under perturbation" to an anyonic syste…
New method interprets quantum many-body snapshots for phase detection.
Quantum theory of curved tetrahedrons yields quantum group intertwiners.
Proposes qIS for quantum generative models, extending classical inception score.
We give a review of the quantum singularity theory of Fan-Jarvis-Ruan and the r-spin theory of Jarvis-Kimura-Vaintrob and describe the work of Abramovich-Jarvis showing that for the singularity A_{r-1} = x^r the stack of A_{r-1}-curves of is canonically isomorphic to the stack of r-spin curves. We prove that the A_{r-1…
Study fermionic theories, their anomalies, and modular transformations.
A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-parti…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean μ and deviation σ, form a 2-dimensional exponential family. In this paper, we show that …
The generalized Legendre transform method of Lindstrom and Rocek yields hyperkaehler metrics from holomorphic functions. Its main ingredients are sections of bundles over the twistor space satisfying a reality condition with respect to antipodal conjugation on the hyperkaehler sphere of complex structure…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and …
High-fidelity quantum simulations demonstrated on short-coherence hardware.