Fundamentals of Measurement-Based Quantum Computation
Measurement-based quantum computation (MBQC) is a recently proposed model of quantum information
processing (QIP) that offers substantial advantages in the implementation of QIP in a variety of physical
systems. There are, however, many aspects of the fundamental theory of MBQC which are not fully
understood. Recent progress has been made in the identification of entanglement properties that families of
resource states need be universal for MBQC (Van Den Nest, Briegel ’06, ‘07). However, many open
questions remain. Are the resource states so far identified, such as graph states and other more recently
discovered states (Gross, Eisert ‘06) the only families which allow universal computation? Are there other
constraints which will restrict the construction of alternative MBQC models? Do different models of MBQC
allow quantum circuits to parallellised to different degrees? Are there non-graph state models of MBQC
better suited to implementations where, generating graph states would be difficult, or where single qubit
measurements were unavailable? What level of experimental imperfection could be tolerated in
implementing scalable MBQC?
This programme of research will aim to answer these questions by developing and generalising the theory of
MBQC. We shall develop new necessary criteria for MBQC resource states and apply them to pure and
mixed, qubit and continuous variable (CV) states. We shall analyse and generalise the dependency structure
of measurements and investigate the degree of parallelisation of algorithms allowed in different models. We
shall investigate generalisations of MBQC e.g. with collective measurements only, and “imperfect” resource
states such as mixed qubit states or finitely squeezed continuous variable states. We aim to employ these new
tools to develop MBQC approaches which offer new practical advantages for particular implementations.
For further information contact Dan Browne