A fault-tolerant quantum computer requires many important components. The different Work Packages of my proposal correspond to different parts of the fault-tolerant quantum computer.
One component that is central to any scalable quantum technology is a quantum error-correcting code. These many body systems are composed of many small quantum devices that work together to protect logical quantum information that is processed by a quantum computer, even if the small devices that make up the code experience errors. It is important to design robust quantum error-correcting codes that can tolerate all of the types of noise the underlying quantum hardware experiences.
A quantum error-correcting code will be supported by a classical computer that runs what is known as a decoding algorithm. A decoding algorithm must efficiently take information from a quantum error-correcting code. Specifically, the information the decoder takes is diagnostic data that indicate what errors may have occurred. The decoder then uses the diagnostic information to determine how to fix the errors the code has experienced. In general, it is difficult to design a decoding algorithm for new codes. Nevertheless, the implementation of good decoders show us the potential of new quantum error-correcting codes, that may perform better than other codes. Furthermore, we can improve the performance of a quantum error-correcting code by developing better decoding algorithms.
Lastly, the information protected by a quantum error-correcting code must also be manipulated to perform quantum algorithms. Furthermore, this information needs to be manipulated without leaving the encoded information vulnerable to errors. As such, we must design logic gates to manipulate the encoded information. In general, it is quite difficult to manipulate quantum information that is encoded with a quantum error-correcting code, and typically a complete 'universal' set of logic gates requires a large number of resources that can be difficult to build in the lab. The design new quantum error-correcting codes, and different types of manipulations.
The three work packages address these different components, with Work Package I designing new decoding algorithms, Work Package II developing logic gates, and Work Package III designing codes that are robust to general sources of noise.
For Work Package I I worked with graduate students at University College London and Yale University to develop a new decoding algorithm for the surface code. This code is now under development at academic institutions including ETH Zurich as well as by the Google Quantum AI research programme. We design a new decoder that is better at correcting a type of noise, known as depolarising noise, that is common for solid state devices that are being developed.
For Work Pacakge II, in collaboration with researchers at the University of Sydney, we produced a publication, published in open-access overlay journal 'Quantum', where we demonstrate a general class of quantum error-correcting codes that we call XP codes. Furthermore, we find this formalism can be used to describe various types of logic gates for this new class of codes.
For Work Package III, in collaboration with researchers at the University of Oxford, we showed how to adapt codes to deal with fabrication defects. These are permanent errors that are common is the production process of the quantum hardware that is now under development to realise quantum error correcting codes. More specifically we showed for the first time how to account for fabrication defects for two-dimensional devices. Indeed, two-dimensional 'on-chip' arrays of qubits are very commonly constructed with solid state architectures.
