arXiv research

Paper solves tracking control for $(x,u)$-flat systems using classical states.

For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.

Sketch Tomography improves quantum state estimation accuracy.

Paper derives explicit formulas for AJ-bracket of tied links.

This work proposes efficient classical training protocols for IQP circuits to train quantum generative models.

We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data to classical data, and thus preserve the interpretability of data under tensor tr…

Global EQG sums boundary states over manifold diffeomorphism classes.

Model financial markets using open quantum systems to understand market imperfections.

New method uses quantum computing to process classical data efficiently.

It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this question would bring important insights to both fields of machine learning and quantum…

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quant…

Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payoffs and portfolios converge under …

Quantum machine learning classification depends on mutual informations between state and parameter spaces.

Novel neural models have been proposed in recent years for learning under domain shift. Most models, however, only evaluate on a single task, on proprietary datasets, or compare to weak baselines, which makes comparison of models difficult. In this paper, we re-evaluate classic general-purpose bootstrapping approaches …

Analogous exponential map defined for Hopf algebras.

We present the quantum model of Bertrand duopoly and study the entanglement behavior on the profit functions of the firms. Using the concept of optimal response of each firm to the price of the opponent, we found only one Nash equilibirum point for maximally entangled initial state. The very presence of quantum entangl…

We employ a solution of the Yang-Baxter equation to construct invariants for knot-like objects. Specifically, we consider a Yang-Baxter state model for the sl(n) polynomial of classical links and extend it to oriented singular links and balanced oriented 4-valent knotted graphs with rigid vertices. We also define a rep…

SGM combines deep learning and planning for robust long-horizon tasks.

Study derives new equation for reserves in non-monotone information scenarios.

Quantum datasets improve QML performance.

Quantum CNNs can be efficiently simulated classically on simple datasets.

A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial $F(a,z)$. In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.

The classical Cohn-Vossen theorem states that two isometric compact convex surfaces in $\mathbb{R}^{3}$ are congruent. In this short note, we generalize the classical Cohn-Vossen Theorem to higher dimensional surfaces in space form $N^{n+1}(K)$ for $n\ge 2$.

Functional brain networks exhibit dynamics on the sub-second temporal scale and are often assumed to embody the physiological substrate of cognitive processes. Here we analyse the temporal and spatial dynamics of these states, as measured by EEG, with a hidden Markov model and compare this approach to classical EEG mic…

New models for insurance claims accounting for delays.

We extend the concept of transfer learning, widely applied in modern machine learning algorithms, to the emerging context of hybrid neural networks composed of classical and quantum elements. We propose different implementations of hybrid transfer learning, but we focus mainly on the paradigm in which a pre-trained cla…

The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. Here this example is shown to be distinct from the same sphere with the reversed orientation. To demonstrate this fact a state-sum invariant for classical knots and knotted surfaces is developed via a cohomology theory of racks a…

Unified framework for learning quantum models from limited measurements.

Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate…

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical…

Quantum statistical models with singularities are studied for state estimation and model selection.

Paper constructs a HOMFLYPT-type invariant for pseudo links.

KalmanNet uses neural networks to improve state estimation in systems with unknown dynamics.

In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension $n > 2$, there exists an embedded surface in $\mathbb R^n$ evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When $n > 3$ this resul…

In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least squares problem, highlight special structure, and show that the classic filtering an…

New methods combine MALA and mGRAD for scalable Bayesian inference in high-dimensional state-space models.

A classical theorem states that the group of automorphisms of a manifold $M$ preserving a $G$-structure of finite type is a Lie group. We generalize this statement to the category of $cs$ manifolds and give some examples, some of which being generalizations of classical notions, others being particular to the super cas…

Rewiring networks using discrete geometry improves GNN training accuracy and reduces runtime.

LLMs struggle to optimize hyperparameters efficiently, but hybrid methods can improve performance.

We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function, we investigate the corresponding recursive infinite-dimensi…

SSDMs generate quantum states directly, outperforming classical methods.

A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty estimates. The converse is true for deep neural networks. In this paper, we propose a hy…

Quantum learning complexity reviewed using information theory.

We extend the state models for Jones and Alexander polynomials of classical links to state models of 2-variable polynomials in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular knots with exactly d double points. These extensions can detect non-invertibilit…

Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather involved for the general case. We provide a proof which is not only short, but a…

Bayesian control prepares GHZ states in Rydberg atoms.

We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.

A reinforcement learning approach prepares quantum squeezed states in open spin systems.