相关论文: Gems of Corrado B\"ohm
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
A theoretical model of computation is proposed based on Lorentz quantum mechanics. Besides the standard qubits, this model has an additional bit, which we call hyperbolic bit (or hybit in short). A set of basic logical gates are constructed…
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic processes is considered…
Verifying fine-grained optimistic concurrent programs remains an open problem. Modern program logics provide abstraction mechanisms and compositional reasoning principles to deal with the inherent complexity. However, their use is mostly…
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…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…
Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the…
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…
Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…
For decades, computational chemistry has been posited as one of the areas in which quantum computing would revolutionize. However, the algorithmic advantages that fault-tolerant quantum computers have for chemistry can be overwhelmed by…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student…
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-orderable, two-generated recursively presented solvable group…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
Motivated by a need for a model of reversible computation appropriate for a Brownian molecular architecture, the $\aleph$ calculus is introduced. This novel model is declarative, concurrent, and term-based--encapsulating all information…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.