Related papers: Symbolic-numerical algorithm for generating cluste…
We demonstrate how correlation functions for non-diagonal operators can be measured with the loop-cluster algorithm for quantum spin models. We introduce the U(1) quantum link model and present the construction of a cluster algorithm for…
The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the…
We study skew-symmetrizable cluster algebras $\mathcal{A}$ associated with unpunctured surfaces $\tilde{\mathbf{S}}$ endowed with an orientation-preserving involution $\sigma$. We give a geometric realization of such cluster algebras by…
Unsupervised machine learning is one of the main techniques employed in artificial intelligence. We introduce an algorithm for quantum-assisted unsupervised data clustering using the self-organizing feature map, a type of artificial neural…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The problem of the determination of the Hilbert-space metric which renders a given Hamiltonian $H$ self-adjoint is addressed from the point of view of applicability of computer-assisted algebraic manipulations. An exactly solvable example…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension)…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic o scillator when $x\to 0$. It is shown that, in the energy basis of…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…
Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ)…