arXiv research

Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.

The financial market entropy is modeled using open quantum systems.

Study on quantum state entanglement using Kaehler manifolds.

Quantum ML predicts data with improved speed and accuracy.

A quantum circuit designed for efficient statistical model preparation and training.

We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These quantum states are contained in a density operator which describes the new quan…

QNA uses quantum-inspired density operators to diagnose market dependence and structural risk.

A quantum state generation method that respects physical constraints.

Quantum entropy scoring improves robust mean estimation and outlier detection.

A new method speeds up quantum state estimation.

We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…

We give a topological formula of the loop expansion of the colored Jones polynomials by using identification of generic quantum sl2 representation with homological representations. This gives a direct topological proof of the Melvin-Morton-Rozansky conjecture, and a connection between entropy of braids and quantum repr…

Constructs QFT on curved surfaces, proving axioms and calculating entropy.

Perelman's Ricci flow emerges in quantum gravity, linking math and physics.

New bounds for quantum circuits depend on how data is encoded.

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate en…

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approxim…

Improved MMWU algorithm achieves instance-optimal regret bound for matrix LEA.

Paper improves variational inference on Boolean hypercube using quantum methods.

It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $Γ=PSL(2,\mathbb{Z})$ [M. Pla…

Although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) it is shown that both are analogous and thus exactly equivalents. The quantum analogue of the replicator dynamics is the von Neumann equation. Quantum mechanics could be used to explain more correc…

Quantum channels' contraction under privacy constraints studied.

RILA learns HQMMs robustly against adversarial corruption.

For a given quantum field theory, provided the area of the entangling surface is fixed, what surface maximizes entanglement entropy? We analyze the answer to this question in four and higher dimensions. Surprisingly, in four dimensions the answer is related to a mathematical problem of finding surfaces which minimize t…

DO-EM framework for quantum models improves generative tasks.

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, p…

By analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently different both are analogous and thus exactly equivalents. The extensions of qu…

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

This review explores entropy applications in data analysis and machine learning.

Study quantifies information flow in neural networks using relative entropy and RG analogy.

Quantum TNCS uses machine learning to efficiently transmit data.

Tensor networks and RNNs are equivalent, improving wave function encoding.

Hybrid classical-quantum framework optimizes portfolio rebalancing with reduced transaction costs.

Geometrically constructs twist-field correlation functions in CFT.

In this paper we consider the space of those probability distributions which maximize the $q$-Rényi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some methods to endow this parameter space with Riemannian metric is presented: the seco…

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman's functionals and derived the corresponding fractional evolution …

Study of supersymmetric AdS solutions using fibred GK geometries.

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of availa…

Ray-Singer torsion measures light degrees of freedom in black hole entropy.

The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions of a variety of input data including natural images, speech signals, and custome…

This study analyzes a non-orientable spacetime model in 1+1D quantum gravity.

This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.

Unified approach for robust and heavy-tailed mean estimation in high dimensions.

Study examines BTZ black hole using information geometry.

q-CNN learns data features through entangled states.

Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A popular problem in {\it quantum state tomography} (QST) is to estimate the unknown l…