Control characterisation of noisy quantum devices

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The current project will characterise the performance of controlled quantum devices in the presence of noise through extensive numerical computations and a new paradigm of control. This is important for emergent quantum technology where noise is a major obstacle. The aims of the project are the numerical characterisation of the operations that can be reached in noisy single and two qubit experiments, the development of estimation techniques and better controls for noise, and a simpler analytical toolbox to describe noisy control operations of single qubits.Quantum technology has the potential to revolutionise science and technology. For example quantum devices that can measure individual nuclear spins seem just about within reach. The main obstacle for such amazing technology is however background noise. Because of a lack of theoretical tools, noise is ignored at the device design and its consequences can only be tested in the actual experiment. The main aim of this proposal is to enable the modelling of the noise already at design stage, thereby allowing to optimize performance and stability by orders of magnitude. The project addresses several ambitious short-term goals by developing noise-resistant and noise-aided methods of control. Using state-of-the-art high performance computers will enable the characterisation of diamond impurities and thereby aid the design of more efficient quantum measurement devices. The PI is already in contact with leading groups who have agreed to share details on the control set-up and parameters. More generally a database of reachable operations in noisy devices and the development of an open source algorithm will make the numerical studies applicable to other implementations of quantum technologies, such as ion traps.The main challenge of controlling noisy systems is the validity of the model in the presence of control. This project will put the modelling of controlled noisy systems on a rigorous theoretical footing. Error bounds will be derived using well established tools from open quantum systems. These bounds will be used to derive a set of criteria under which control frequencies the weak coupling limit Lindbladian remains a good model. We will then know which approximation is justified in the experimental case studies. The interesting consequence of the control dependence is that properties of the bath which would be considered unobservable in standard process tomography will become visible through controls. Explicit methods for estimating noise parameters will be discovered this way.Finally from a theoretical perspective it is also important to develop better analytical tools for noisy control. This has been elusive so far because of the complicated mathematical structure of quantum operations. The aim of the present proposal is to consider the new paradigm of mixed controls, e.g. applying pulses chosen randomly from a set of pulses, and thereby imposing a convex structure in the reachable operations. This will substantially simplify noisy control in low-dimensional systems. It also paves the way to implement so-called non-decomposable operations, which were previously considered unreachable for controlled quantum devices, and which received considerable attention recently.