Near Term Quantum Computation

Fault tolerant quantum computing will change fundamentally our conception of computing but is at the very least decades away. This is a consequence of the overhead brought about by the need to do Quantum Error Correction. In order to study quantum error correcting

thresholds, assumptions about the noise model are made in order that the problem becomes tractable. In this thesis, we investigate and test the accuracy of one of these error models, the Pauli Twirling Approximation in the five qubit quantum error correcting code.

Secondly, we investigate two aspects of quantum computing before quantum fault tolerance. The first aspect is a proposed near term quantum processor that uses tune-able couplings in superconducting quantum devices and can naturally simulate real and symmetric Hamiltonians. We show that in fact this process can be turned into a universal computational device as we can prove that it can simulate in any complex Hermitian matrix. We do this by proving a new decomposition of lie groups. The second aspect of near term

quantum computation is one that has been afforded to the quantum computing community as public quantum processors have been made available to the general public. We use these devices to study entanglement monotones of GHZ and cluster states.