Related papers: Integrable clusters
Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…
A new proof of Imprimitivity theorem for transitive systems of covariance is given and a definition of square-integrable representation modulo a subgroup is proposed. This clarifies the relation between coherent states, wavelet transforms…
Cluster number counts offer sensitive probes of the dark energy if and only if the_evolution_ of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding…
The construction of partially compactified cluster algebras on coordinate rings is handled by using codimension 2 arguments on cluster covers. An analog of this in the quantum situation is highly desirable but has not been found yet. In…
For almost two decades, it has been believed that the quantum statistical properties of bosons are preserved in plasmonic systems. This idea has been stimulated by experimental work reporting the possibility of preserving nonclassical…
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding…
Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…
In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were…
In this paper, we introduce the enough $g$-pairs property for a principal coefficients cluster algebra, which can be understood as a strong version of the sign-coherence of the $G$-matrices. Then we prove that any skew-symmetrizable…
Multiple quantum coherences are typically characterised by their coherence number and the number of spins that make up the state, though only the coherence number is normally measured. We present a simple set of measurements that extend our…
This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements?…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
For each positive integer n, we define a polynomial in the variables z_1,...,z_n with coefficients in the ring $\mathbb{Q}[q,t,r]$ of polynomial functions of three parameters q, t, r. These polynomials naturally arise in the context of…
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…
In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce the notion of cluster equivalence for these algebras, based on whether their generalized cluster categories are equivalent. We are…
Clustering multimorbidity has been a global research priority in recent years. Existing studies usually identify these clusters using one of several popular clustering methods and then explore various characteristics of these clusters,…
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive…
It is shown that the joint measurements of some physical variables corresponding to commuting operators performed on pre- and post-selected quantum systems invariably disturb each other. The significance of this result for recent proofs of…