New Developments in Quantum Algorithms

Diederik Aerts

Jarosław Adam Miszczak

Quantum information theory allows us to use quantum mechanics resources for processing and sending information. Since the rules of quantum mechanics are in many aspects counterintuitive, the development of new quantum algorithms and protocols is complicated. At the moment only a few algorithms exist which can be executed on a quantum computer with significant improvement in speed or memory usage. \n \nThe main goal of this thesis is to describe the methods of using quantum programming languages for developing new quantum algorithms. We present the original implementation of a classical game where quantum programming was used to develop and analyse quantisation of the game. We also show how quantum data types, ie. data types allowing for storing superposition of values, can be used to develop new quantum algorithms.

Richard Cleve

Abstract : The goals of this project are as follows: discover new quantum algorithms, develop novel paradigms for constructing quantum algorithms, develop complexity-theoretic results that relate to quantum algorithms, and develop theoretical approaches for the implementation of quantum algorithms. Building on the pioneering work of Shor and Grover, the field of quantum algorithms has developed substantially, providing numerous insights about the mechanisms underlying quantum algorithms, as well as the limitations of these algorithms. Recent work on novel paradigms for designing quantum algorithms (e.g., quantum walks and adiabatic computing), as well as theoretical advances relating algorithms to physical implementations (e.g., efficient error-correction techniques) point to promising directions for future development. The focus of this research is on searching for new algorithms and investigating the limitations of quantum information processing. This work is complemented by an investigation of quantum error-correction -- the accuracy threshold for a variety of error models -- that is focused on reducing overhead for implementations.

Peter W. Shor

Dan-Alexandru Teodoraș, Eduard C. Popovici, George Dan Suciu +1 more

In the context of the development of quantum technology, most asymmetric encryption algorithms managed to be broken using Shor's algorithm, while symmetric encryption algorithms, such as AES-256, are believed to be unbroken for the moment, Grover's algorithm has been able only to reduce AES brute force attack time to its square root. This paper proposes to present how Quantum technology can affect current security algorithms and analyze how it can be used to improve our data protection by developing new algorithms. Quantum cryptography alongside Quantum key distribution could be a deal-breaker by using new encryption algorithms and providing new solutions to different cryptographic tasks that are known to be impossible by using normal computers. In the end, it will be discussed how the concept of quantum teleportation could provide new, faster, and much more secure solutions in telecommunication compared with the ones based on radio technologies.

Peter W. Shor