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Research Activities in QuNaT

The research of the QuNaT group members is predominantly focussed on architectures and implementations of quantum computers. Apart from abstract graph-state architectures, we study optical and solid-state implementations and their noise properties.

Graph-state quantum computing (return to top)

Quantum information science is a rapidly developing field connecting quantum physics and the theories of information and computation. It spans the disciplines of physics, computer science and mathematics, and experimental implementations have been performed in a wide range of areas, from optics and solid state physics to NMR. The field has emerged from the realisation that the quantum state of a physical system, for example, an atom or a light field, can be used to represent information, and conversely, information itself is always stored within some physical system, and thus should obey physical laws. A quantum computer would harness the non-classical features of quantum mechanics to process information in a new way. Certain problems could then be solved much more efficiently than on a standard classical computer. A famous example of such a problem is the factorisation of large numbers, but more importantly for scientific research, a quantum computer could efficiently simulate quantum systems. This would be a powerful tool for many disciplines including physics, chemistry and materials science. For a full-scale quantum computer to be built many difficult challenges must be overcome. While experiments in the wide variety of proposed implementations are making good progress, new theoretical developments are essential. The standard approach to quantum computation proceeds in close analogy with standard classical computation. A register of two-level quantum systems represent the quantum bits or qubits. Quantum algorithms are performed as a sequence of single and two-qubit operations. Recently, however, a very different model of quantum computation was developed named one-way quantum computation. This proceeds in two stages. Initially a special entangled quantum state is created over a large number of qubits. This state is called a cluster state or graph state. Single qubit measurements on this resource state then project the unmeasured qubits into the desired computational output state.The quantum algorithm is then specified in the structure of the entanglement together with the choice of basis for the measurements. This offers practical advantages for a number of experimental settings. Furthermore, there are good indications that this model is particularly robust to errors and decoherence.

Optical quantum computing with photons and matter qubits (return to top)

Quantum computing with linear quantum optics has the advantage that the smallest unit of quantum information (the photon) is potentially free from decoherence: The quantum information stored in a photon tends to stay there. The downside is that photons do not naturally interact with each other, and in order to apply two-qubit quantum gates such interactions are essential. In 2001, Knill, Laflamme, and Milburn (KLM) constructed a protocol in which probabilistic two-photon gates are teleported into a quantum circuit with high probability. Subsequent error correction in the quantum circuit is used to bring the error rate down to fault-tolerant levels.

The nonlinear sign gate from the KLM proposal. It is the work horse of linear optical quantum computing, and the teleportation trick can be employed to render this gate near-deterministic.

Several improvements of the protocol have been proposed, leading to ever smaller overhead cost on the computation. A number of these improvements are based on cluster-state quantum computing, and probably the most resource-efficient in the absence of noise is by Browne and Rudolph.

In order to build a real quantum computer based on linear optics, single-photon sources, and photon detection, the design must be able to deal with errors: The unavoidable errors in practical implementations should not erase the quantum information that is present in the computation. What are the types of errors that can occur in the different stages of the quantum computation? We can group them according to the optical components: detection errors, source errors, and circuit errors. A comprehensive review of linear optical quantum computing and the practical hurdles that will be encountered in designing these devices is given by Kok et al.

The component that is, at this point, most difficult to make is the optical quantum memory: A photon must be able to enter as well as exit the memory with very high fidelity. It might therefore be easier to engineer these systems such that they support coherent single-qubit operations. This way, we can redefine our qubits as isolated static systems, and we have circumvented the problem of qubit loss. When these matter qubits emit a qubit-dependent photon, they can in turn be entangled using techniques from linear optical quantum computing. It was shown by Barrett and Kok that such an architecture can support scalable quantum computing, even with current realistic components.

Two qubits in individual cavities with an L-shaped level structure can be entangled with very high fidelity, even if the photo-detectors are inefficient. The 50:50 beam splitter erases the which-path information of the photon. The resulting entanglement can be used to create cluster states.

We study the noise properties of these (and related) systems, and how the noise affects the creation of cluster states for quantum computing.

Solid-state entanglement (return to top)

We are investigating solid state implementations of QIP, particularly those in which the qubit is embodied by the spin of an electron. A number of systems are being studied. First, we are looking at using quantum dots to house the electron spin, and at finding methods to manipulate it using optical methods (and so exploiting the spin-exciton coupling that exists in such systems). Second, carbon materials (including fullerenes, nanotubes and diamond) can contain the impurity spin and we are developing methods to couple these spins both optically and via conduction electrons in the surrounding material. The research covers a range of modern quantum mechanical techniques, such as quantum optics and master equations, spin-boson models and the renormalization group. An ultimate aim of the research is to understand how a small quantum system interacts with a larger environment about which our knowledge is limited. This could lead to insights into the processes of quantum decoherence and measurement.

We have a number of external collaborations including DAMTP (Cambridge University), Hewlett Packard Laboratories (Bristol), University of Queensland (Brisbane, Australia) and the University of California (Santa Barbara, USA). These support our theory and also provide groups which are performing experiments to help us to test our predictions.