While the adiabatic theorem provides a useful theoretical handle to understand quantum computing in continuous time, solving hard problems adiabatically would require an exponentially long runtime and therefore unless P=NP will require either an exponentially long coherence time or a mechanism to restore coherence. On the other hand, algorithms which only succeed with an exponentially small probability may still be useful on more realistic devices, for which coherence time either does not scale, or scales only mildly.

We find that even the simplest of this algorithm, a quantum walk which consists of evolution with a fixed Hamiltonian can provide better scaling on artificial spin glass problems than unstructured Grover-like search, this implies that the algorithm is using the structure of the problem. When parameters are swept over time rather than held constant, the scaling becomes dramatically better, and competitive with state of the art quantum algorithms.

I will discuss the theoretical reasons why these algorithms perform so well, which relate to the relative energy expectation of different terms of the Hamiltonian, and give several examples to demonstrate how the theoretical tools we have developed work, these results have now been reported in our recent pre-print [https://arxiv.org/abs/2007.11599].

Finally, I briefly discuss the outlook of the field of quantum computing as a whole and what make promising use cases for quantum computers, based on the discussion in another recent pre-print [https://arxiv.org/abs/2006.05846].

About the Speaker

Nicholas Chancellor is an EPSRC UKRI Innovation fellow at Durham University. Nicholas specializes in continuous time quantum computing, in particular quantum annealing and hybrid quantum/classical algorithms using continuous time hardware. Nicholas helped pioneer the reverse annealing technique which is currently available on the commercial quantum annealers produced by D-Wave Systems Inc. with his single author paper ‘Modernizing Quantum Annealing using Local Searches’. He also wrote one of, if not the first papers showing the use of quantum annealers for thermal sampling.

Prior to being awarded a fellowship, Nicholas worked as a postdoc for Viv Kendon. Prior to that he was a postdoc at UCL, where hw focused on experimental quantum annealing, this postdoc was supervised by Andrew Green and Gabriel Aeppli, and he also worked closely with Paul Warburton. Nicholas Chancellor attained his PhD from the University of Southern California under the supervision of Stephan Haas. Up to date information about Nicholas’s work can be found at: http://nicholas-chancellor.me.