Supervisors:

Viv Kendon (Durham University)

Florian Mintert

CONTINUOUS-TIME QUANTUM-COMPUTING (CTQC)
Continuous time quantum computing (CTQC) is a class of quantum computing strategies in which a classical problem is encoded into a classical Hamiltonian on the qubits such that the low-energy states encode its solution. Then, instead of applying quantum gates, a continuous time evolution (possibly including non-unitary dynamics) is applied to drive the qubits towards these solution states. This model of computation includes as special cases: closed-system adiabatic quantum computation, computation by (continuous-time) quantum walk, open-system-dominated quantum annealing, and many types of special purpose quantum simulation. A hybrid strategy that takes advantage of features from all these will provide a quantum advantage for practical computation.

 A very wide range of important optimisation and sampling problems, in finance, microbiology, aerospace, big data, neural networks and many other areas, are well-suited to these CTQC strategies. Furthermore, hardware being designed and built for one of these types of computation should be suitable for a wider range of problems than those for which it was originally designed.

 The project has begun with a detailed numerical study of determining spin-glass ground-states, a problem whose typical hardness acts as a suitable model of real-world optimisation problems. Furthermore, through a combination of numerical and analytical methods, we aim to more firmly establish the theoretical underpinnings of CTQC, study what can be done with existing hardware (e.g quantum simulators), and produce new, more flexible hardware designs.