## MQC: Methods for Quantum Computing

MQC: Methods for Quantum Computing

European Research Council (ERC) Advanced Grant

01/05/2013-30/04/2018

Project reference: 320731

Principal Investigator:

Andris Ambainis

Abstract:

Quantum information science (QIS) is a young research area at the frontier of both computer science and physics. It studies what happens when we apply the principles of quantum mechanics to problems in computer science and information processing. This has resulted in many unexpected discoveries and opened up new frontiers. Quantum algorithms (such as Shors factoring algorithm) can solve computational problems that are intractable for conventional computers. Quantum mechanics also enables quantum cryptography which provides an ultimate degree of security that cannot be achieved by conventional methods.

These developments have generated an enormous interest both in building a quantum computer and exploring the mathematical foundations of quantum information. We will study computer science aspects of QIS. Our first goal is to develop new quantum algorithms and, more generally, new algorithmic techniques for developing quantum algorithms. We will explore a variety of new ideas: quantum walks, span programs, learning graphs, linear equation solving, computing by transforming quantum states. Secondly, we will study the limits of quantum computing. We will look at various classes of computational problems and analyse what are the biggest speedups that quantum algorithms can achieve. We will also work on identifying computational problems which are hard even for a quantum computer. Such problems can serve as a basis for cryptography that would be secure against quantum computers. Thirdly, the ideas from quantum information can lead to very surprising connections between different fields. The mathematical methods from quantum information can be applied to solve purely classical (non-quantum) problems in computer science. The ideas from computer science can be used to study the complexity of physical systems in quantum mechanics. We think that both of those directions have the potential for unexpected breakthroughs and we will pursue both of them.