Towards fault-tolerant quantum computing with minimal resources.

This project concerns the future of high-performance computing, which is waiting for a quantum revolution. Advances in conventional processor clock speed have slowed and almost plateaued, and so traditional computer development has shifted to building machines with more cores instead of faster cores. On these multicore machines, many programs can run simultaneously and huge speed-ups are possible when parallel programming. But many computational tasks can not be parallelized or have exponentially growing processing demands. Quantum computing is an entirely different paradigm capable of efficiently dealing with some of these very hard computational tasks. The theory is that through exquisite control of quantum systems, such as individual electrons or photons, we can can execute algorithms following a quantum rather than binary logic. These quantum algorithms need fewer clock cycles than classical counterparts, and even exponentially fewer! The reality is that perfect control of quantum systems is impossible. The UK is home to some of the most advanced quantum computing laboratories, and the Oxford Ion trap group has achieved single processing steps at 99.9% perfection. This might yet be improved to 99.99%, but then unavoidable interactions between Ions and their surrounding make further progress unlikely.

Whilst impressive, this limits us to only a few hundred elementary steps before a catastrophic computational failure. This project develops important fault-tolerance techniques that can, despite inevitable experimental limitations, ensure reliable quantum computations of any length. Fault-tolerance already underpins many modern technologies; it allows lightly scratched Blu-ray discs to play movies, and communication through solar winds to the Voyager spacecraft at the edge of our solar system. This comes at some cost. High-end graphics cards are fault-tolerant but need 12.5% of their memory for this purpose. Fault-tolerant quantum computing is more challenging by nature and has to deal with more errors. Current estimates are upward of 99% of all quantum memory being used to provide fault-tolerance. Providing enough memory for a useful quantum computation would be a monumental engineering challenge.

The aim of this project is find a software solution. To find better approaches to fault tolerance and reduce these monstrous overheads to a more manageable amount. The biggest recent advances have been to use ideas from topology to encode information. Topology is a global feature. The real Earth and a flat Earth would both look flat on an everyday level, but are globally distinct. Quantum information can similarly be stored in global degrees of freedom, without leaving any evidence in local patches. The donut, or torus, topology has been the engine driving improvements in fault-tolerance theory. Before these improvements, the prerequisites for fault-tolerance were so stringent that experiments could not meet them. With the pressing urgency of reducing fault-tolerance overheads, this project again looks to topology for inspiration. This time stranger and more exotic topologies will be used as models upon which to build fault-tolerant quantum computers at lower resource costs. This project will develop numerical simulations of these topologically fault-tolerant computers, to compare different approaches and find the most cost-effective method. For optimal performance, the topology of fault-tolerance software must be reflected in the hardware design of a quantum computers. In collaboration with experimentalists, the project will produce realistic blueprints for the first generation of fault-tolerant quantum computers.

Fault-tolerance theory is one of the central pillars of quantum computing, and essential to any experimental realizations. As such, immediate academic beneficiaries and commercial beneficiaries include all those developing quantum computing hardware. In particular, I will aid and complement the development of fault-tolerance protocols for the EPSRC funded quantum technology hubs. Through this project I will develop software that would form an essential complement to quantum computing hardware. Furthermore, beginning with my PDRA and collaborators, I will begin to train a larger group of fault-tolerance experts that would form the backbone of future generations of quantum computer software engineers. Beyond my immediate collaborators, I will foster closer ties between the physics, computer science and mathematics communities, through a series of European conferences and workshops on the general theme of fault-tolerant quantum computing.

In the commercial sector companies already invested in quantum computing include IBM, Microsoft, Google, Lockheed Martin, Nokia, Toshiba and Sandia Labs. This list will rapidly grow as quantum computers come closer to market. A primary objective of this project is to present a clear picture of the hardware requirements for fault-tolerant quantum computing, which is essential to help guide both academic and commercial hardware development. The project will also provide sophisticated software necessary to govern the fault-tolerance process. We have seen in the modern IT industry that the value of the software market has substantially outgrown the hardware market. With this in mind, the project will build the foundations of a budding quantum software economy that could thrive quite independently of whether the UK becomes a global exporter of quantum computing hardware.

The research will be exceptionally useful to policy-makers as WP4 assesses just how well UK experimental efforts are doing against the necessary fault-tolerance benchmarks. The project will generate advice on how large a quantum computer must be to compete with traditional computers, and so what timelines are realistic. This will manage expectations of the public and policy makers on realistic time scales in what is often an over-hyped area. This information will be communicated through public talks, exhibitions and visual media developed to portray the ideas behind fault-tolerance quantum computing.