The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.

The emergence of quantum information technologies with potential application across diverse industrial, consumer and technical domains has thrown into relief the need for practical approaches to their governance. Technology governance must balance multiple objectives including facilitating technological development while meeting legal requirements, normative expectations and managing risks regarding the use of such technology. In this paper, we articulate a variety of idealised governance models and approaches for synthesising these complementary and sometimes competing objectives. We set out a comparative analysis of quantum governance in the context of existing models of technological governance. Using this approach, we develop an actor-instrument model for quantum governance, denoted the ‘quantum governance stack’, across a governance hierarchy from states and governments through to public and private institutions. Our model sets out key characteristics that quantum governance should exhibit at each level in the stack, including identification of stakeholder rights, interests and obligations impacted by quantum technologies and the appropriate instruments by which such impacts are managed. We argue that quantum governance must be responsive based on (a) the state of technology at the time; (b) resource and economic requirements for its development; and (c) assessments and estimates of the near-term and future impacts of such technology. Our work provides a pragmatic introduction to quantum governance by (a) specifying a taxonomy of governance actors and instruments and (b) providing examples of how different stakeholders within the stack might implement governance responses to quantum information technologies. It is intended for use by stakeholders in government, industry, academia and civil society to help inform their governance response to the quantum technology revolution.