Implementation of quantum LDPC codes and fault-tolerant logic gates in physical architectures

Quantum error correction (QEC) is a tool for developing quantum technologies that are robust against unavoidable errors due to unwanted interactions with the environment. QEC can be used to construct actively-corrected quantum memories [1], and the consideration of fault-tolerant gates in tandem leads to development of fault-tolerant quantum computation. Within the field of classical error correction, low density parity check (LDPC) codes are well-known linear error-correcting codes that have been studied for decades and are widely used in modern communication networks. They are characterised by a sparse parity check matrix (PCM), with key metrics being the number of physical bits, encoded bits, and distance of the code. Quantum LDPC (qLDPC) codes aim to maximise the same metrics under the different set of restrictions imposed by the quantum nature of the errors. In recent years, there have numerous developments in constructing good quantum error-correcting codes [2]: those characterised by linear (or near-linear) scaling of code distance and encoding rate with the number of physical qubits. However, these rates are only approached asymptotically [3, 4, 5], which makes their performance and implementation in real systems either unfeasible or unknown. There also exist trade-offs when considering good codes and physical restrictions, e.g. constraints on the code locality which in turn bound the encoding rate and distance [6, 7]. The aim of the PhD projects will be to work towards building good quantum error-correcting codes tailored to real architectures. The structure of the PhD is given as a series of projects under the umbrella of achieving fault tolerance and good qLDPC codes. This would involve numerical simulation of qLDPC codes, as well as understanding their construction before tailoring them towards realistic implementation. Beyond code construction, fault-tolerant implementations of logic gates will also be considered due to the crucial part they play in quantum information processing.

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.