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Quantum algorithms and the foundations of quantum computation

Final Report Summary - QAQC (Quantum algorithms and the foundations of quantum computation)

Quantum computing is a new research field at the frontier of both computer science and physics. It studies how to apply quantum mechanics to solve problems in computer science and information processing. The principles of quantum mechanics are radically different from those of conventional (classical) physics and these differences can be very useful for computer science.

A quantum computer is a computer that functions according to the principles of quantum mechanics. It has been shown that quantum computers will be able to solve problems that are thought to be hard for classical computers (for example, factoring and the discrete logarithm problem). This discovery was of great importance for cryptography because the security of today's systems for data encryption (e.g. RSA and Diffie-Hellman) is based on the assumption that factoring and discrete logarithm are hard. Thus, building a quantum computer would make today's systems for data encryption insecure.

Quantum computers would also be very useful for search problems. In 1996, Lov Grover invented an algorithm for quantum computers that solves a generic search problem quadratically faster than any classical computer. This generic search algorithm can be applied to any search problem.

The goal of this international reintegration grant (IRG) is to support the return of Andris Ambainis to University of Latvia, after studying and working in USA and Canada for nine years. While working in USA and Canada, Andris Ambainis has become one of world's leading experts in the theory of quantum computing.

The goal of the project was that Andris Ambainis will start a new research group in quantum computing at university of Latvia. The research of this group will focus on three directions:
- Design of new quantum algorithms;
- Understanding the limits of quantum computing;
- Understanding the fundamental properties of quantum states.

The goals of the project have been successfully accomplished. Over the four years of Marie Curie (MC) IRGs, Andris Ambainis has established a research group consisting of himself, a postdoctoral fellow and six PhD students. The group is actively conducting research in the computer science aspects of quantum computing and has become one of leading European research groups in this area.

The group has produced a number of interesting research results, for example:
- a new algorithm for solving systems of linear equations on a quantum computer;
- a new method for designing quantum algorithms based on learning graphs (developed by MC Fellow's PhD student Aleksandrs Belovs, this method is one of most interesting recent developments in quantum algorithms in the world);
- a limit on how large speedups can be achieved by quantum algorithms for symmetric functions;
- a quantum generalisation of Lovasz local lemma, an important result in combinatorics with many applications to theoretical computer science.

Research results of the group have been presented in leading international conferences in theoretical computer science (such as Symposium on theory of computing (STOC) and international colloquium on automata, languages and programming (ICALP)).

Prof Ambainis' research group is also coordinating an seventh framework programme (FP7) collaborative research project that involves eight universities and research institutes in seven European countries, with many of the leading European researchers in quantum information being part of this project.