P89: The dynamics of quantum machine learning

Project abstract

The tensor network description of quantum mechanical systems has a tremendous similarity with deep learning networks used for machine learning. The exponential size of Hilbert space and the very large size of data sets present similar challenges, moreover, the hierarchical nature of our observed world - both quantum mechanical and classical – has led to the construction of tensor networks and deep learning networks that embody this. It is natural to use this link between quantum mechanical systems and deep learning to develop new methods of performing quantum machine learning.

This project first focused upon the translation of established and trained classical deep learning networks to quantum machines (for example, Google’s bristlecone machine, to which Prof Green will have access via a recently established collaboration with Google/UCL/Bristol).

Next, we aimed to develop new methods of training such quantum machine learning networks. Training and optimisation is (aside from the adiabatic algorithm) a fundamentally non-unitary process. The only way to achieve such non-linearity in a quantum mechanical system was through measurement or coupling to the environment. At present, most proposals for optimisation of a quantum neural network involve employing it as a subroutine in a classical programme that adjusts the settings of the quantum network after each measurement. We investigated the extent to which judicious measurement on a subset of ancilla quantum bits can be used to mimic the effects of coupling to a zero-temperature bath and allow new – all quantum – methods of optimising quantum neural networks.

This was a theoretical project that combined analytical and numerical calculations. It heavily relied upon strong computational skills, involving the development of algorithms suitable for quantum computers. This project was at the intersection of machine learning (neural networks) and advanced quantum many-body simulation (tensor networks). We considered the use of tensor networks as a compressed representation of a descriptor in machine learning, which requires optimization. On quantum computers, this optimization follows a ‘time-dependent’ unitary evolution, which we aim to turn into a non-unitary optimization via coupling with an auxiliary measurement system.

The student was required to develop knowledge and implement novel computational algorithms for tensor networks and machine learning (supported by second supervisor, George Booth), while access and development of time-evolution algorithms suitable for quantum computers will be supported by Prof. Green, who supported the theoretical underpinning of the project, and supervised analytical insights and development required for the project.

References

Reference 1: E Miles Stoudenmire, D Schwab “Supervised learning with tensor networks” Advances in neural information processing systems 29 (NIPS 2016)  

Reference 2: Huggins et al “Towards quantum machine learning with tensor networks” arXiv 1803.11537  

Reference 3: E Grant et al “ Hierachical quantum classifiers’’ arXiv 1804.03680  

Reference 4: Hallam et all ‘’Compact neural networks based upon MERA’’ arXiv 1711.03357  

Reference 5: U Schollwoeck, “DMRG in the age of MPS”, arXiv: 1008.3477