Related papers: The Z1: Architecture and Algorithms of Konrad Zuse…
Turing's famous 'machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach and provide a framework for computing with objects of any…
These are notes for the course CS-172 I first taught in the Fall 1986 at UC Berkeley and subsequently at Boston University. The goal was to introduce the undergraduates to basic concepts of Theory of Computation and to provoke their…
Incorporating Quantum Computers into High Performance Computing (HPC) environments (commonly referred to as HPC+QC integration) marks a pivotal step in advancing computational capabilities for scientific research. Here we report the…
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…
We propose an implementation of a quantum computer to solve Deutsch's problem, which requires exponential time on a classical computer but only linear time with quantum parallelism. By using a dual-rail qubit representation as a simple form…
We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ans\"atze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided,…
The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute…
Quantum computers must achieve large-scale, fault-tolerant operation to deliver on their promise of transformational processing power [1-4]. This will require thousands or millions of high-fidelity quantum gates and similar numbers of…
In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…
The Inscriptions which were on the Back Cover of the Antikythera Mechanism were the Users Manual of the Antikythera Mechanism. In the Back Cover Inscription Part 1 text, the Presentation, Position, and Operation of the outer parts of the…
Recent analyses have calculated the minimal thermodynamic work required to perform a computation pi when two conditions hold: the output of pi is independent of its input (e.g., as in bit erasure); we use a physical computer C to implement…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
The rapid proliferation of generative AI has fundamentally altered the landscape of introductory computer science education. Traditional methods that prioritize syntax memorization and writing code from scratch are challenged by tools that…
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties.…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient.…
As a potential revolutionary topic in future information processing, mechanical computing has gained tremendous attention for replacing or supplementing conventional electronics vulnerable to power outages, security attacks, and harsh…
The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using `rewrite rules' to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic…
Turing's famous `machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach to computing with objects of any finite type. Both…