English
Related papers

Related papers: The Computational Complexity of Ball Permutations

200 papers

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random…

Statistical Mechanics · Physics 2024-06-21 Andrea De Luca , Chunxiao Liu , Adam Nahum , Tianci Zhou

We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…

Formal Languages and Automata Theory · Computer Science 2021-08-17 Stefan Hoffmann

Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…

Group Theory · Mathematics 2025-05-06 Attila Egri-Nagy , Chrystopher L. Nehaniv

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

Quantum Physics · Physics 2009-11-07 Carlton M. Caves , Christopher A. Fuchs , Ruediger Schack

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…

Quantum Physics · Physics 2009-10-30 Emanuel Knill , Raymond Laflamme , Wojciech H. Zurek

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…

Quantum Physics · Physics 2016-10-07 Thomas Vidick , John Watrous

The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named…

Quantum Physics · Physics 2021-04-28 Elisa I. Goettems , Thiago O. Maciel , Diogo O. Soares-Pinto , E. I. Duzzioni

While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…

Quantum Physics · Physics 2018-01-01 Jacob Miller , Stephen Sanders , Akimasa Miyake

We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis…

Quantum Physics · Physics 2020-11-11 Martin Hebenstreit , Richard Jozsa , Barbara Kraus , Sergii Strelchuk

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…

Logic · Mathematics 2019-11-19 Nathanael L. Ackerman , Cameron E. Freer , Daniel M. Roy

Constraint programming (CP) is a powerful tool for modeling mathematical concepts and objects and finding both solutions or counter examples. One of the major strengths of CP is that problems can easily be combined or expanded. In this…

Discrete Mathematics · Computer Science 2025-01-29 Ruth Hoffmann , Özgür Akgün , Christopher Jefferson

Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the…

Quantum Physics · Physics 2008-02-03 Haiqing Wei , Xin Xue

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…

Quantum Physics · Physics 2007-05-23 Pawel Wocjan , Shengyu Zhang

Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…

Quantum Physics · Physics 2015-05-20 Javier Rodriguez-Laguna , Silvia N. Santalla

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…

The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…

Quantum Physics · Physics 2007-05-23 Benjamin Levi , Bertrand Georgeot

We propose a framework to study models of computation of indeterministic data, represented by abstract "distributions". In these distributions, probabilities are replaced by "amplitudes" drawn from a fixed semi-ring $S$, of which the…

Computational Complexity · Computer Science 2014-12-24 Niel de Beaudrap

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s).…

Artificial Intelligence · Computer Science 2012-04-18 Toby Walsh

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Combinatorics · Mathematics 2016-11-01 Franck Gabriel

Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…

Quantum Physics · Physics 2024-04-17 Leonardo Banchi , Jason Luke Pereira , Sharu Theresa Jose , Osvaldo Simeone