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.
Enhances quantum sensing by eliminating multiple oscillations in field amplitude estimation.
Unified approach for learning quantum operations from measurements.
New method infers unknown parameters in quantum sensing with high probability.
We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.
We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use the unsupervised TN machine learning algorithm to obtain the entangled state $|Ψ…
Introduces Quantum Data Center for quantum era benefits.
Quantum cellular automata form a homology theory.
Quantum-enhanced barcode decoding and pattern recognition outperforms classical methods.
New quantum state reconstruction method accelerates convergence.
Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact quantum group is necessarily commutative as a C \ast algebra i.e. Q = C(G) for som…
We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…
The paper shows compatibility between two quantum maps for surfaces and 3-manifolds.
We show that an isometric action of a compact quantum group on the underlying geodesic metric space of a compact connected Riemannian manifold with strictly negative curvature is automatically classical, in the sense that it factors through the action of the isometry group of . This partially answers a q…
If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the co-tangent bundle, then it is proved that the quantum group is necessarily commut…
Quantum Gaussian processes enable scalable quantum learning.
A decentralized online quantum cash system, called qBitcoin, is given. We design the system which has great benefits of quantization in the following sense. Firstly, quantum teleportation technology is used for coin transaction, which prevents from the owner of the coin keeping the original coin data even after sending…
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a two-dimensional Riemannian manifold. Under the assumption that the strip is asym…
This review covers quantum computing applications in finance and blockchain.
Binary operations on algebras of observables are studied in the quantum as well as in the classical case. It is shown that certain natural compatibility conditions with the associative product imply the properties which usually are additionally required. In particular, it is proved that locality of a Loday bracket on s…
Program connects quantum computing and topological field theories.
In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-t…
Quantum trace maps for surfaces are shown to be compatible under triangulations.
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. …
This work constructs a finite-dimensional projective representation for a quantum Teichmüller model.
Study calculates quantum hyperbolic invariants for figure-eight knot complement, finding it either 0 or half the volume.
We investigate the perturbative aspects of Rozansky-Witten's 3d -model using Costello's approach to the Batalin-Vilkovisky (BV) formalism. We show that the BV quantization (in Costello's sense) of the model, which produces a perturbative quantum field theory, can be obtained via the configuration space method of reg…
Study shows mass distribution of random holomorphic sections follows a central limit theorem.
This is a survey of our work on Quantum Hyperbolic Invariants (QHI) of 3-manifolds. We explain how the theory of scissors congruence classes is a powerful geometric framework for QHI and for a `Volume Conjecture' to make sense.
Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.
Geometrically decomposes Kähler functions on toric manifolds.
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…
Study of bound states in quantum layers with confining potentials.
We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's co…
New quantum invariants for 3-manifolds with boundary defined via virtual links.
This paper provides a construction of a quantum statistical mechanical system associated to knots in the 3-sphere and cyclic branched coverings of the 3-sphere, which is an analog, in the sense of arithmetic topology, of the Bost-Connes system, with knots replacing primes, and cyclic branched coverings of the 3-sphere …
Hybrid tensor networks improve machine learning by combining quantum and classical methods.
We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the …
The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…
Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum tra…
For A a primitive 2N-root of unity with N odd, the Witten-Reshetikhin-Turaev topological quantum field theory provides a representation of the Kauffman skein algebra of a closed surface. We show that this representation is irreducible and we compute its classical shadow, in the sense of earlier work of the authors (arX…
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, smooth surface embedded in . We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not tot…
Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to perform any task efficiently in a changing environment, and it is fundamental for ma…
Analyzes quantization of flux observables in gauge theories.
Bernstein processes are Brownian diffusions that appear in Euclidean Quantum Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation associated with these processes allows one to obtain relations between stochastic processes (Lescot-Zambrini, Progress in Probability, vols 58 and 59). More recentl…
Quantum modularity proved for a knot manifold.
Quantizes geodesic lengths in Teichmüller spaces using algebraic methods.
Homological model for quantum representations of mapping class groups.
Given a family of Dirac operators with vanishing spectral flow we construct a thin-invariant rank-one field theory in the sense of Turner and Willerton arXiv:math.AT/0201116. Our construction of the field theory generalizes the one of the index gerbe by Lott, arXiv:math.DG/0106177, and it also complements the relation …