Related papers: Integrable clusters
We consider nonlinear recurrences generated from the iteration of maps that arise from cluster algebras. More precisely, starting from a skew-symmetric integer matrix, or its corresponding quiver, one can define a set of mutation…
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision…
We show that in case a cluster algebra coincides with its upper cluster algebra and the cluster algebra admits a grading with finite dimensional homogeneous components, the corresponding Berenstein-Zelevinsky quantum cluster algebra can be…
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable…
We provide a concrete realization of the cluster algebras associated with Q-systems as amalgamations of cluster structures on double Bruhat cells in simple algebraic groups. For nonsimply-laced groups, this provides a cluster-algebraic…
Clustering is grouping of data by the proximity of some properties. We report on the possibility of increasing the efficiency of clustering of points in a plane using artificial quantum neural networks after the replacement of the two-level…
Analog quantum computation offers a route to machine learning using controllable physical dynamics as a computational resource. However, many existing approaches rely on task-specific protocols or observables that are difficult to access…
Coherent states possess a regularized path integral and gives a natural relation between classical variables and quantum operators. Recent work by Klauder and Whiting has included extended variables, that can be thought of as gauge fields,…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
Graph clustering groups entities -- the vertices of a graph -- based on their similarity, typically using a complex distance function over a large number of features. Successful integration of clustering approaches in automated…
Quantum Phase slips are dual process of particle tunneling in coherent networks. Besides to be of central interest for condensed matter physics, quantum phase slips are resources that are sought to be manipulated in quantum circuits. Here,…
This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still…
The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases established in [6], and…
We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
Recent cosmological measurements tend to confirm that the fine structure constant {\alpha} is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's…