Related papers: $q$-Analogs for Steiner Systems and Covering Desig…
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they…
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of…
Open quantum systems are a rich area of research in the intersection of quantum mechanics and stochastic analysis. By considering a variety of master equations, we unify multiple views of autonomous and controlled open quantum systems and,…
Divisible design graphs were introduced in 2011 by Haemers, Kharaghani and Meulenberg. In this paper, we introduce the notion of $q$-analogs of divisible design graphs and show that all $q$-analogs of divisible design graphs come from…
According to the $q$-series method, a short proof for Hou and Sun's identity, which is the $q$-analogue of a known $\pi$-formula, is offered. Furthermore, $q$-analogues of several other $\pi$-formulas are also established in terms of the…
We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions.
In recent years, the role of crystal symmetries in enriching the variety of TIs have been actively investigated. Higher-order TIs are a new type of topological crystalline insulators that exhibit gapless boundary states whose dimensionality…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
We give an excess theorem for spherical 2-designs. This theorem is a dual version of the spectral excess theorem for graphs, which gives a characterization of distance-regular graphs, among regular graphs in terms of the eigenvalues and the…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
With the rapid advancement of quantum computing technology, there is a growing need for new debugging tools for quantum programs. Recent research has highlighted the potential of assertions for debugging quantum programs. In this paper, we…
Due to the difficulties of implementing joint measurements, quantum illumination schemes that are based on signal-idler entanglement are difficult to implement in practice. For this reason, one may consider quantum-inspired designs of…
Many existing algorithms for model checking of infinite-state systems operate on constraints which are used to represent (potentially infinite) sets of states. A general powerful technique which can be employed for proving termination of…
For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
We formulate and study, in general terms, the problem of quantum system identification, i.e., the determination (or estimation) of unknown quantum channels through their action on suitably chosen input density operators. We also present a…
Let A_{R,q} denote a family of covering codes, in which the covering radius R and the size q of the underlying Galois field are fixed, while the code length tends to infinity. In this paper, infinite sets of families A_{R,q}, where R is…