Title:

Characterisation and Rapid Purification of a Superconducting Charge Qubit

The work of this thesis focuses on stochastic methods for the simulation of superconducting
charge qubits, also known as Cooper pair boxes, which are promising
candidates for large scale quantum information processing. To aid nonphysicists,
a brief outline of the structure of quantum mechanics is provided using theÃ‚Â· Dirac
formalism.
Using the so called 'Backreaction effect', we consider if any information can
be obtained regarding the qubit behaviour, through detecting the changes observed
in the frequency spectrum of the coupled biasing circuitry, modelled as a
dissipative oscillator circuit. The process of modelling dissipative quantum systems
is described, however an alternative approach called 'quantum trajectories'
is used rather than the traditional CalderiaLeggett model, as the time evolution
of a single 'trajectory' represents the evolution of an individual system coupled
to a noisy environment. Through the noise generated by an excited qubit, the
energy level structure of the qubit can be probed with a microwave drive field, by
observing the noise power within the biasing circuit. We consider a biasing circuit
of unusually high resonant frequency which can drive the qubit, this creates
frequency splitting features that would not normally be observed.
Weak measurement is also examined as this is closely related to the stochastic
'quantum trajectories', where the measurement is recorded by the observer rather
than lost to an environment. Weakly measuring a qubit does not completely
collapse it and therefore 'quantum feedback' may be employed to alter the qubit
controls favourably. In particular we consider the problem of purifying a weakly
measured system rapidly; given a qubit in the completely mixed state what is
the best feedback to become confident in the actual qubit state quickly. There
are two optimal feedback protocols proposed by Jacobs [1] and by Wiseman and
Ralph [2] for purifying qubits that have ideal controls. However, we adapt these
protocols for the charge qubit, whose finite Hamiltonian resources and nonzero
ax tunnelling term means the Bloch vector can not be easily held in the optimal
location.
