Related papers: Computing holes in semi-groups and its application…
The construction of quantum computer simulators requires advanced software which can capture the most significant characteristics of the quantum behavior and quantum states of qubits in such systems. Additionally, one needs to provide valid…
Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…
We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…
Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…
A wide variety of problems in combinatorics and discrete optimization depend on counting the set $S$ of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic. We take a tour…
Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across…
The statistics of quantum transport through chaotic cavities with two leads is encoded in transport moments $M_m={\rm Tr}[(t^\dag t)^m]$, where $t$ is the transmission matrix, which have a known universal expression for systems without…
An algorithm is given for finding the solutions to 3SAT problems. The algorithm uses Bienstock's reduction from 3SAT to existence of induced odd cycle of length greater than three, passing through a prescribed node in the constructed graph.…
We considered the problem how to handle the exploding number of possibilities to be sorted into irreducible classes by using a clustering tool when its input capacity cannot accommodate the total number of the possibility. Concrete…
Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining…
This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…
We examine the computational complexity of problems in which we are given generators for a partial bijection semigroup and asked to check properties of the generated semigroup. We prove that the following problems are in AC$^0$: (1)…
Because of a formal equivalence with the partition function of an Ising chain, the semiclassical traces of the quantum baker map can be calculated using the transfer-matrix method. We analyze the transfer matrices associated with the baker…
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
The Set Partitioning Problem is a combinatorial optimization problem with wide-ranging applicability, used to model various real-world tasks such as facility location and crew scheduling. However, real-world applications often require…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…