Quantum Computation: Foundations, Security, Cryptography and Group Theory
Lead Research Organisation:
University of Glasgow
Department Name: School of Computing Science
Abstract
Quantum computation is based on computers which operate on the level of quantum mechanics rather than classical electronics. The advantage of this is that in quantum mechanics entities can be simultaneously in many different positions at once: and this allows states of a quantum computer to behave in some ways like a stack of parallel states. This parallel stack does not unfortunately come without strings and, because of the physics of quantum mechanics, it is very difficult to find out what is in any such stack at a particular time: so reading the output of a quantum computer is not easy. Some powerful quantum algorithms have been developed: for example by Shor to factor integers much faster than conventional algorithms can. However the number of such algorithms that we know is not growing very rapidly. One reason for this is that we do not have a systematic understanding of how to build up quantum computing algorithms and indeed do not have a comprehensive library of algorithms for very basic functions and procedures for building from them. The main aims of this project are to construct such a systematic foundation for quantum computation and to establish procedures for basic processes.We shall test our success in these objectives by attempting to construct algorithms for problems which arise in group theory. This area of mathematics provides an endless array of algorithmic problems at all levels of difficulty, so is a good test bed for a potential computation system. We shall also consider how to extend the analysis of cryptographic systems from classical schemes to quantum schemes. In particular this is expected to allow us to build an automated voting process which cannot be tampered with or broken into, by the people who run it.
Organisations
People |
ORCID iD |
Simon Gay (Principal Investigator) |
Publications
A.S. Davidson T
(2011)
Formal Analysis of Quantum Systems using Process Calculus
in Electronic Proceedings in Theoretical Computer Science
Davidson T
(2011)
Formal Analysis of Quantum Systems using Process Calculus
Davidson Tim
(2012)
Model Checking for Communicating Quantum Processes
in INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING
Davidson Timothy A. S.
(2012)
Formal verification techniques using quantum process calculus
Description | My contribution to the project concerned the application of "formal methods" to quantum information processing systems. The aim of formal methods is to develop systematic techniques and tools to analyse the correctness of communication and computational systems. During the project I made significant progress with a formal methods technique known as "model-checking", which has been highly successful for the analysis of classical (non-quantum) systems. |
Exploitation Route | Research on quantum model-checking has continued, and will form the basis for future projects; one is being submitted in the near future. |
Sectors | Digital/Communication/Information Technologies (including Software) |