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Topological Quantum Science |
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We traditionally classify order in many body systems through the lens of Landau theory where the symmetry at the microscopic level is broken to a lower symmetry in the ground states, e.g. ordering of spins along one direction in the Ising model. In topological systems the opposite occurs, the ground states have emergent symmetries not present in the microscopic equations of motion. This has enormous consequences amoung them being that this state of matter is characterized by more than just the energy and few body correlation functions but also by the entropy of subsystems in the ground state.
Early on TO states were proposed as ground states for high temperature superconductors and for fractional quantum Hall states. It was also realized that such states could support excitations that behave as anyons in two dimensions. In normal three dimensional space (and in fact in any higher dimensional space) particles come in two types bosons and fermions according to whether the wavefunction accumulates a +1 or -1 phase under exchange of a pair of identical particles. In two dimensions more possibilities arise such as the accumulation of an arbitrary phase for the case of Abelian anyons, or a matrix valued action for non-Abelian anyons. In a landmark 1997 paper A. Kitaev showed that by manipulating the anyons one could perform quantum computation in an essentially error free way. Such a physically protected quantum computer would be a tremendous boon for experimental realizations because it would avoid some of the large resource overheads of more standard techniques that use active error correction.
There are a variety of physical media that generate topologically ordered systems and anyons including: two dimensional electron gases in the fractional quantum Hall regime, and 2D and 3D spin lattices realized with Josephson junction arrays or trapped atoms/molecules in optical lattices. |
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At the Quantum Materials and Applications (QMApp) Lab, we are interested in growing nanoscopic diamond particles which contain single atomic impurities (for example Nitrogen, Silicon or Nickel). In doing so, we are able to isolate single quantum states within the diamond, and use them for many interesting, cutting edge experiments. For example, the diamond impurities can be made to emit single light particles which are used in unbreakable cryptography schemes, or the light emitting from a single nitrogen atom could be used as a tool to measure the presence of a single electron.
At the Quantum Materials and Applications (QMApp) Lab, we are interested in growing nanoscopic diamond particles which contain single atomic impurities (for example Nitrogen, Silicon or Nickel). In doing so, we are able to isolate single quantum states within the diamond, and use them for many interesting, cutting edge experiments. For example, the diamond impurities can be made to emit single light particles which are used in unbreakable cryptography schemes, or the light emitting from a single nitrogen atom could be used as a tool to measure the presence of a single electron. |
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Optical systems are a promising candidate for encoding and manipulating quantum information.
- Photons interact very weakly with their environment (polarization qubits have the lowest intrinsic decoherence of any physical system explored to date) and the sources of decoherence are well characterised.
- The polarisation state of photons can be easily manipulated with passive waveplates.
- Optical qubits are a natural choice for quantum communication, hence they seamlessly combining computation and communication tasks.
The challenge with optical qubits is creating multi-qubit gates and designing fault-tolerant architectures. There are several choices for the qubits including using polarisation states of photons, the path the photon takes, and using coherent states. Typically gates on the qubits are done nondeterministically using particular resource states and teleportation. There are also different ways of putting all the elements together for a computation such as a circuit model, optical cluster states and using optical nonlinearities.
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A milestone for a first generation quantum device would be to simulate complex dynamics beyond the capacity of a classical computer. This would involve mapping some model problem such an interacting two dimensional electron gas into a register of two state quantum systems (qubits), guiding the register by the appropriate control fields, and finally implementing a suitable measurement. For many systems of interest, the size and complexity of the model Hamiltonian prohibits an accurate analytic or computational treatment.
A quantum simulator could overcome such limitations because the interactions that the device is intended to emulate could be engineered into the device itself. We are interested in designing protocols for analogue and digital quantum simulators with focus on implementations in atomic/molecular and optical (AMO) systems. One promising approach is to use atoms or molecules trapped in an optical lattice which is a periodic potential produced by interfering standing waves of laser light. Such systems can simulate highly correlated spin lattice models with unknown properties using building blocks with well known physical properties. Possible constructions include platforms for quantum cellular automata and nearest neighbor spin lattice Hamiltonians in 1D, 2D, and 3D. A particularly compelling pursuit is the connection between protected quantum memory and topologically ordered spin states.
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Global Control: Individual quantum systems are very fragile and to be useful in quantum devices (for computation or for other purposes), they must be accurately controlled. Currently the standard approach used is that one must develop technology capable of controlling each and every individual quantum system within the device. This has proven possible for small quantum devices (8 ions), after years of very intense effort. The challenge of scaling up these control solutions to quantum devices containing hundred and perhaps millions of quantum systems seems incredibly daunting. We are interested in developing ways of controlling quantum systems where one needs only address the quantum components in a massively parallel fashion, i.e. where one gives up the ability to address individual quantum systems within the device. This method, known as global addressing, has been shown to be capable of performing universal quantum computation.
Robust Control: developing strategies for quantum control in the presence of uncertainties. Such a theory would make it possible to design devices built out of large numbers of imperfect components, and to be confident of their correct functioning. |
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In the development of quantum information processing many groups around the world are beginning to create small scale quantum devices. To ensure the quality of these devices, effective characterisation is necessary. This allows us to ascertain to what degree these devices are performing their designed operations. This task is even more critical during development where good diagnostics are crucial to understand and overcome the physical processes that may limit the device's function.
Unfortunately, the complexity of these devices is beginning to outstrip our ability to characterise and debug them. This problem will rapidly become critical as the devices become larger. The aim is to develop practical quantum state and device characterisation techniques which will immediately benefit the development of this exciting field. |
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The early years of quantum mechanics were focussed on understanding "closed" physical systems; they were assumed to be isolated from their surroundings. But this is an idealization as all physical system are to a greater or less "open", which, remarkably, has consequences that are crucial to our understanding of the character of the observed physical world. Open quantum systems exhibit irreversible behaviour, (as do their classical physics counterparts). They evolve in one direction only, with the implied links to the perception of an "arrow of time" and as such are important in understanding processes ranging from the spontaneous emission of light by atoms, to the transport of heat, and of information. The properties of open systems play an essential role in determining how the observed classical world emerges from its quantum mechanical underpinnings via the process known as decoherence. |
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