Supervisors:

• Professor Vlato Vedral, University of Oxford
• Professor Myungshik Kim, Imperial College London

Measurement Based Quantum Computing with Topological Phase Transitions

A modern idea to implement quantum computations is to consider a highly entangled many-bodied system and to perform computations by making single measurements on the system. An example of which is the cluster state model [1] which makes single measurements on a specially prepared highly entangled system. This system is advantageous over the quantum circuit model of quantum computation because all qubit-qubit interactions are initiated before the computation takes place. This is beneficial because it is difficult to entangle two particles on demand. Unless this can be done with certainty then problems will occur in a computation. If a system can be entangled beforethe computation takes place as in a cluster state computation then these problems can be alleviated because all the entanglement will be produced beforehand. After which only single qubit measurements need to be made. However it still stands that a system needs to be entangled.

Quantum order can be considered as a description of the entanglement of a many body system when it is in the ground state [2]. Looking at the entanglement within many body systems it may be possible to discover a system that already exhibits entanglement that can be harnessed. If this is the case then it may be possible to use the entanglement to perform computations. This would be advantageous over a cluster state because the entanglement would already exist and it would not be necessary to generate any entanglement at all. This can be analysed using duality mappings.

Duality mappings offer a method of looking at systems by transforming one representation of a system into another representation where the problem may be easier to solve. This offers a method for extracting properties of the phase diagram beyond the perturbative regions [2].

References
[1] H. J. Briegel, R. Raussendorf, Phys. Rev. Lett., 86 901
[2] W. Son, et al. Entanglement, topological order and quantum criticality in a cluster state model,
[3] X. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press (2004))