Periodic Reporting for period 1 - NPhOMaQuCo (New Phases of Matter for Quantum Computation) Reporting period: 2021-09-01 to 2023-08-31 Summary of the context and overall objectives of the project The development of a large-scale quantum computer will enable us to solve problems that are not currently solvable with ordinary computing technology. For instance, it will help us to model different materials and chemical reactions at the microscopic level.As such the discovery of such a machine may help us understand molecular processes that enable us to design better batteries or more efficient solar cells. Presently, it is very difficult to build a large scale quantum computer using quantum devices that are inherently faulty. The field of research of this project is quantum error correction. The goal of which is to design a quantum computer that is scalable, even when constructed with noisy components. The overarching goal of this proposal is to design better fault-tolerant systems, to make it easier to build a scalable quantum computer. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far 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. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The results described under the previous heading have had the following impact.In regards to Work Package I - We used our new decoding algorithm to produce numerical results showing that our practical decoder outperforms standard decoding methods for this code. Upon completing our publication which is now in preparation, we expect our decoder will have an impact on the decoding software used at institutions now developing this code (e.g. ETH Zurich and Google Quantum AI). Furthermore, given that I am carrying out this project as a supervised project, my expertise in this field, and our results, are also disseminated by training activities.In regards to Work Package II - The XP codes we developed extend the standard stabilizer formalism that is commonly used to describe quantum error-correcting codes. We have found that this formalism gives us a new way of describing codes with a rich set of gates. Moreover, the formalism can be used to simulate the types of errors that are common when we perform logic gates with quantum error correcting codes. I therefore expect that this formalism will be helpful in designing new codes with different logic gates in the future, and for simulating logic gates to determine their performance. Ultimately, the formalism we have developed may show us how to design better fault-tolerant architectures capable of universal quantum computing.In regards to Work Package III - Our results showed for the first time how, in principle, a two-dimensional system is robust to the fabrication defects that will inevitably occur during the manufacturing process. This is true only using the new protocol we designed. I have been invited to talk about this work at a number of venues including the Sydney Quantum Information Theory Workshop, and in a seminar at TU Delft. I have also discussed these ideas at length with my industrial collaborators. Given the interest I have received, I expect that adapations of our proposal will be adopted to deal with fabrication defects that occur on various types of hardware that are now being produced in the laboratory. Related documents drawing4f copy.jpg
