Why molecular electron spins?
By encoding a qubit within a molecule one can ensure that each bit is identical, allowing accurate control over each of the qubits’ properties. Furthermore, the chemistry of the chosen molecule may be exploited to generate large qubit arrays through molecular self-assembly. An electron spin qubit is advantageous because it can be precisely manipulated (by pulsed Electron Paramagnetic Resonance or EPR) and initialized through cooling.

Why endohedral fullerenes?
One of the most remarkably robust examples of electron spin within a molecule is that of a nitrogen atom trapped inside a spherical fullerene (termed N@C60). I have studied the coherence time (quantum information lifetime) of a qubit encoded within this electron spin system and found this to have a coherence time of 0.25 milliseconds (the longest for any moleculare electron spin) . Typical single qubit quantum logic gate operation times are 20 nanoseconds. This yields a “figure-of-merit” (the coherence time divided by the gate operation time) in excess of 10,000, a commonly-cited threshold for fault-tolerant quantum. Whilst this figure is already much larger than many leading qubit candidates, there may also exist alternative surrounding matrices for N@C60 which will lead to even longer coherence times, and thus further enhance the case for embodying quantum information within this endohedral fullerene.

High-fidelity pulsed EPR
I have been studying the capabilities of pulsed electron spin resonance spectrometers for quantum information processing (QIP) through new error-measuring algorithms, and used error-correcting sequences to produce high-fidelity single-qubit gates on electron spins. Based on these results, I am helping to develop a new pulsed EPR facility in the Physics Department at Oxford which has been specifically designed with quantum computation in mind. This spectrometer will also be compatible with molecular/solid-state hybrid devices able to combine transport measurements with high-fidelity pulsed EPR.

Fullerene dimers: two qubits
Studies on fullerene dimers (two-qubit systems) will illustrate which types of spin-spin coupling may be exploited for the multiple-qubit logic gates crucial to any kind of quantum computation. An ideal spin-spin interaction would yield a two-qubit gate time which is significantly slower than a single-qubit gate, but substantially faster than the decoherence processes. A successful implementation of a conditional-NOT gate on an endohedral fullerene dimer would be an important step in developing a fullerene-based quantum computer.

Graph state quantum computation
Graph states are really great for quantum computing! Entanglement between a number of qubits is generated in advance (this can be achieved optically using qubits in separate cavities), and it is then consumed as a resource for the quantum computation.

Single-molecule magnets (SMMs)
These are systems in which single molecules are capable of obtaining a permanent magnetisation, and are another molecular electron spin system being considered as a potential qubit candidate.

Acknowledgements
In addition to working with groups of Andrew Briggs and Arzhang Ardavan in the Materials and Physics departments at Oxford University, I have enjoyed a very productive collaboration with Alexei Tyryshkin and Steve Lyon at Princeton University, supported by the Oxford-Princeton Link Fund.