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THEORETICAL QUANTUM COMPUTATION AND INFORMATION

 

Program Manager:
Prof Gerard Milburn - University of Queensland

Participating UQ Researchers:
Prof Michael Nielsen
Dr Tim Ralph

John Paul Barjaktarevic
Ms Jennifer Dodd
Mr Andrew Hines
Mr Mohan Sarovar

Participating UM Researchers:
A/Prof Lloyd Hollenberg
Mr Austin Fowler

Collaborating Researchers:
Dr Manny Knill, Los Alamos National Laboratory, USA
Dr Raymond Laflamme, Los Alamos National Laboratory, USA
Dr Daniel James, Los Alamos National Laboratory, USA
Dr Carl Caves, The University of New Mexico, USA

Linear optics quantum computation
Until recently it was thought that QC with photons required large third order (Kerr type) optical nonlinearity. Such interactions are typically slow and noisy. We recently discovered, in collaboration with Knill and Laflamme at Los Alamos, that single photon sources, passive linear optics and particle detectors are sufficient for implementing reliable quantum algorithms. Feedback from the detectors to the optical elements is required for this implementation. Without feedback, non-deterministic quantum computation is possible. We are currenlty investigating optical circuits for small scale algorithms such as Grover's algorithm and error correction.

Ion trap QC
Ion traps enable as few as one ion to be held in a oscillating electromagnetic field for long periods. Laser cooling enables the ions to be placed in the ground state of their lowest order collective vibrational mode. Two internal electronic states of the ions are used to encode the information. External lasers, directed at individual ions, enable the internal states to entangle the vibrational mode and the electronic state of many ions. Following the suggestion of Cirac and Zoller for an ion trap quantum computer, a number of labs are actively pursuing ion traps for studying large quantum entanglement and information processing.

A variety on interacting many body systems may be 'synthesised' in an ion trap QC architecture, for example the Tavis-Cummings model can be realised in a linear ion trap of N ions with the bosonic degree of freedom appearing as the quantised collective centre-of-mass motion. If each ion is coupled to the vibrational motion using an identical external (classical) laser detuned to the first red-sideband transition, the symmetry is such that the electronic degree of freedom for the ions can be described as a collective spin (N) and the reversible dynamics is well described by the TC model. The TC model is known to exhibit important nonlinear quantum effects including a quantum phase transition in which the (zero temperature) ground state undergoes a morphological change as a parameter is varied and averages of intensive quantities undergo a bifurcation.
We recently proposed a new approach to ion trap QC using operator valued geometric phases. This approach has recently been implemented in the NIST ion trap experiment (see Nature, 422, 412 - 415 ( 2003).

We have used this new approach to show how a class of models exhibiting a quantum phase transition can be simulated on an ion trap QC.



 

 


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