Related papers: Three Puzzles on Mathematics, Computation, and Gam…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…
Merging disciplines has led to incredible learnings and breakthroughs throughout history, including the discovery of quantum computing: a cross between computation and quantum physics. In this paper, I will discuss how we can cross quantum…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
Over the past few years, quantum computers and quantum algorithms have attracted considerable interest and attention from numerous scientific disciplines. In this article, we aim to provide a non-technical, yet informative introduction to…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
Quantum Computing (QC) is often challenging for beginners due to its abstract concepts and mathematical foundations. This paper explores the use of gamification to support the learning of introductory QC concepts. To investigate this,…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…
In this paper three unrelated problems will be discussed. What connects them is the rich methodology of classical probability theory. In the first two problems we have a complete answer to the problems raised; in the third case, what we…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…