相关论文: What is the point of computers? A question for pur…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
This chapter aims to provide next-level understanding of the problems of the world and the solutions available to those problems, which lie very well within the domain of neural computing, and at the same time are intelligent in their…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however,…
Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on…
Analog computers can be revived as a feasible technology platform for low precision, energy efficient and fast computing. We justify this statement by measuring the performance of a modern analog computer and comparing it with that of…
The objective of this paper is to describe a development of an innovative approach to enable students studying science, technology, engineering, and mathematics (STEM) to apply the concepts learned in physics and mathematics to engineering…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Recent advancements in quantum computing are leading to an era of practical utility, enabling the tackling of increasingly complex problems. The goal of this era is to leverage quantum computing to solve real-world problems in fields such…
Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its…
With a growing interest in quantum technology globally, there is an increasing need for accessing relevant physical systems for education and research. In this paper we introduce a commercially available on-site quantum computer utilizing…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…