Related papers: Combining Determinism and Indeterminism
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades,…
The main aim of this paper is twofold: (1) Suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions --- a way of writing an…
We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on…
We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
The aim of this work is to reduce the complexity of the available algorithms for computing the generator sets of a semigroup ideal by using the Hermite normal form. In order to achieve it we introduce the concept of decomposable semigroup.…
Real-world clinical problems are often characterized by multimodal data, usually associated with incomplete views and limited sample sizes in their cohorts, posing significant limitations for machine learning algorithms. In this work, we…
We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…
We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results…
In this paper we study structural properties of LV-degrees of the algebra of collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. We construct atoms…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…