Exploring quantum enhancements from indefinite causality and time-reversing gates

The notion that events happen in defined causal orders, where one event temporally follows another, is innate to our understanding of the classical world we live in. However, the laws of quantum mechanics allow the strict assumption of a definite causal order to be relaxed, giving rise to events with indefinite causal orders arising from quantum superpositions of causally ordered processes [1]. Indefinite causality can be exploited to achieve advantages in quantum computation [2], quantum communication [3,4], quantum metrology [5], and other information processing tasks [6]. It also has implications for the foundations of quantum theory and concepts in quantum gravity. The aim of this project is to investigate the fundamental concepts underlying indefinite causality and explore potential new quantum advantages that can be harnessed, both on theoretical and experimental fronts. In this hybrid project, I will first work on (i) the theoretical aspect of formulating physical processes able to violate so called "causal inequalities" [7] (bounds on the correlations between events which hold whenever these take place in a well-defined causal order), and (ii) theoretical advantages that can be achieved from indefinite causality, before moving onto experimental work using integrated photonics. On the experimental side, I will perform experiments to illustrate the advantage of
indefinite causality in quantum metrology, using a silicon photonic chip that has already been fabricated and is now ready for characterisation. Based on the results obtained in the first (theoretical) phase of this project, this project may also include first prototype experiments demonstrating the violation of causal inequalities, or indefinite causal order processes involving 4 parties. Alongside the work on indefinite causality, I will also study a conceptually related concept, namely, the possibility of temporally reversing unknown unitary operations [8,9] and its applications for quantum technologies. I will extend the theoretical work I started in Project A for a protocol to perform quantum key distribution (QKD) noiselessly along a channel that applies unitary noise. I will also design an on-chip experiment to demonstrate the protocols in Ref. [8,9].

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.