Implementing optimal Control with principla Component Analysis

Optimal control, and in particular quantum optimal control [1], is the practice of quantifying the application of 'controls', generally EM fields, to a quantum system to drive it from an initial quantum state into a desired final state. The control is termed optimal if it performs the desired task while describing a minimum in some parameter space, generally either time taken, or energy expended. These problems (beyond massively simplifying approximations like the rotating wave approximation for two level systems [2]) tend to not admit analytical solutions so must be numerically derived, and subsequently tested on real systems. There may be several control strategies for a system, and these can be cluster educing, for example, density-based clustering [5]. Controls may tend to have similar properties in their cluster, robustness for example can be analysed on a cluster scale. The controllers can also be decomposed into an effective eigen basis using PCA, giving a sharp reduction in the necessary dimensionality of the optimisation problem. This dimensionality reduction is vital for closed loop control in a physical system where the infidelity of a control may be measured [3]. This was studied theoretically for a BEC system [3], driving from the ground to second excited state. The goal would be to extend the BEC modelling to a more complex system (with noise) which we have physical access to, such as Alex Clark's. This builds from the previous work but should provide a recipe for other finding controllers for and clustering/reducing dimensionality of general systems. This should result in identification of control strategies with an idea of their robustness which can feasibly be close loop optimised. This would then be implemented on the system to hopefully show performance gains and characterise the improvements for different routes. This should then further provide for a comparison of controls between different transitions where naively there should be considerable overlap. The second aspect of this project involves a shaken lattice interferometer, this is a matter-based interferometer with atoms trapped in a phase-modulated optical lattice [4]. The key advantage over a fountain approach is the physical footprint, with lattice pseudo momentum providing the state splitting. The goal would be to extend Carrie's (and Meagan's) previous work in a shaken lattice interferometer to higher degrees of freedom. This modelling would incorporate up to a six-axis sensor including rotation sensing, however such a device is substantially more involved than purely separable axis. When modelled with the necessary propagation and controls this can translate to implementation in a real system either in Boulder or Bristol.

Our ambitions for the impact of the Quantum Engineering CDT are simple and clear: our PhD graduates will be the key talent that creates a new, thriving, globally-competitive quantum industry within the UK. In Bristol we will provide an entire ecosystem for innovation in quantum technologies (QT). Our strong and diverse research base includes strengths going from quantum foundations to algorithms, experimental quantum science to quantum hardware. What makes Bristol unique is our strong innovation and entrepreneurship focus that is deeply embedded in the entire culture of the CDT and beyond. This is reflected in our recent successful venture QTEC, the Quantum Technologies Enterprise Centre, and our Quantum Technologies Innovation Centre (QTIC), which are already enabling industry and entrepreneurs to set up their own QT activities in Bristol. This all occurs alongside internationally recognised incubators/accelerators SetSquared, EngineShed, and UnitDX.

At the centre of this ecosystem lies the CDT. We will not just be supplying existing industry with deeply trained talent, but they will become the CEOs and CTOs of new QT companies. We are already well along this path: 7 Bristol PhD students are currently involved in QT start-ups and 3 alumni have founded their own companies. We expect this number to rise significantly when the first CDT cohort graduates next year (2 students have already secured start-up positions). Equally, it is likely that our graduates will be the first quantum engineers to make new innovations in existing classical technology companies - this is an important aspect, as e.g. the existing photonics, aerospace and telecommunications industries will also need QT experts.

The portfolio of talent with which each CDT graduate will be equipped makes them uniquely suited to many roles in this future QT space. They will have a deep knowledge of their subject, having produced world-leading research, but will also understand how to turn basic science into a product. They will have worked with individuals in their cohort with very different skills background, making them invaluable to companies in the future who need these interdisciplinary team skills to bring about quantum innovations in their own companies. Such skills in teamworking, project management, and self-lead innovation are evidenced by the hugely successful Quantum Innovation Lab (QIL). The idea and development of QIL is entirely student-driven: it brings together diverse industrial partners such as Deutsche Bank, Hitachi, and MSquared Lasers, Airbus, BT, and Leonardo - the competition to take part in QIL shows the hunger by national industry for QT in general, and our students' skills and abilities specifically. With this in mind, our Programme has been co-developed with local, UK, and international companies which are presently investing in QT, such as Airbus, BT, Google, Heilbronn, Hitachi, HPE, IDQuantique, Keysight, Microsoft, Oxford Instruments, and Rigetti. The technologies we target should lead to products in the short and medium term, not just the longer term. The first UK-wide fibre-based quantum communication network will likely involve an academic-industrial partnership with our CDT graduates leading the way. Quantum sensing devices are likely to be the product of individual innovators within the CDT and supported by QTIC in the form of spin-outs. Our graduates will be well-positioned to contribute to the advancement of quantum simulation and computing hardware, as developed by e.g. our partners Google, Microsoft and Rigetti. New to the CDT will be enhanced training in quantum software: this is an area where the UK has a strong chance to play a key role. Our CDT graduates will be able to contribute to all aspects of the software stack required for first-generation quantum computers and simulators, the potential impact of which is shown by the current flurry of global activity in this area.