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Distributed Quantum Computation. A Measurement-Based Approach

Friday, 21 October, 2005 - 16:00
Campus: Brussels Humanities, Sciences & Engineering campus
Faculty: Science and Bio-engineering Sciences
D
2.01
Ellie D'Hondt
phd defence

This work is in essence an exploration of the distributed quantum
computing paradigm. Our main philosophy is that we need to take a
bottom-up approach in order to identify and investigate the different
programming concepts at work in this domain. We advocate the use of
the measurement calculus as the basis from which to evolve a formal
framework for distributed quantum computing. In this framework we
investigate the expressiveness of the paradigm, the primitive operations
on which protocols are based, and we reason about the knowledge of
distributed parties in a protocol.

In a first approach, we develop the global view, a formal model for
synchronous distributed computations which is closely related to the
measurement calculus and inherits many of its structures. We also
establish an alternative asynchronous agent-based model called the local
view and develop its formal semantics. Though reminiscent of process
algebraic models, the local view is specifically tailored to quantum
distributed computations. Next, we identify primitive operations for
distributed quantum computation, and investigate their properties and
relationships in the local view. Rather than summing up a series of specific
protocols involving distributed parties, we have chosen to include
operations that lie at the basis of such protocols. At the same time, we
expose the flexibility and usability of the formal frameworks developed
earlier. We propose protocols for quantum leader election and distributed
consensus, and prove that in anonymous networks these tasks can be
solved exactly only with specific quantum resources. Finally, we define
quantum knowledge and develop a formal framework in which to
investigate epistemic and temporal features of distributed quantum
protocols. While we rely on structures developed earlier, our notion of
quantum knowledge makes sense more generally in any agent-based
model of quantum networks. In this way, we are able to analyse
distributed primitives encountered earlier from a knowledge-based
perspective.