At its most fundamental level, computation relies on being able to use physical components to represent and manipulate abstract information. Representation of information can be accomplished in two ways:
(1) Digital computing, in which all information is represented in a discrete way, ones and zeros.
(2) Analog computing, in which some of the information is represented as continuous variables.
Classical computing is currently dominated by digital technology, e.g. desktops, laptops, and smart phones are all governed by digital technology. Within living memory, hybrid computation has dominated, calculations where performed by analog slide rules, supplemented by digitallike pen and paper calculations. Algorithms based on emulating natural (analog) processes are powerful computational tools. An example would be simulated annealing, where solutions to optimization problems are found by simulating a cooling process. A more sophisticated algorithm such as parallel tempering, which involves 'swapping' systems at different temperatures, is even more powerful than simulated annealing and has made it obsolete.
Quantum computing:
(1) Uses the quantum nature of the world we live in to produce more powerful computation.
(2) Has proven to be better at solving some problems than any nonquantum approach.
(3) Quantum computing devices are just getting to the stage of being useful. Therefore, the design of algorithms which can get the most performance out of small and imperfect devices is imperative.
Quantum annealing:
(1) Is a quantum analogue of simulated annealing, which uses quantum mechanics to aid calculations.
(2) Quantum annealing already has experimental implementations, which are commercially available, e.g. devices produced by DWave systems Inc. have been purchased for use by Google, NASA, and Lockheed Martin.
(3) Quantum annealers are especially suited to optimisation and machine learning problems, such as the travelling salesperson problem.
My project:
(1) I will develop protocols, which are hybrids between analog (like continuoustime quantum computation which harness fundamental laws of physics) and classical digital computation, to make computations more powerful.
(2) The algorithms that I will develop will run on hybrid partclassical, partquantum hardware.
(3) I will also develop algorithms based on continuoustime quantum computing methods such as quantum random walks.
(4) Additionally, I will develop algorithms based on simulations of analog quantum systems. They can be run either on digital quantum computers, based on discrete 'gates', or on classical machines. I will develop techniques, which work on many quantum computing platforms and will be useful regardless of relative rates of development.
The project will take a threepronged approach:
(1) I will construct more sophisticated hybrid algorithms, for instance, analogues of parallel tempering rather than simulated annealing.
(2) Then, I will provide proofofprinciple that these algorithms have an advantage over current methods.
(3) Finally, I will develop implementations on real devices and case studies for realworld industrial problems.
