The worlds most advanced quantum technologies rely for a large part on the control
and manipulation of quantum states of light. From entanglement swapping to Boson
sampling, linear optical devices such as beam splitters and integrated photonic circuits
are essential for accomplishing key tasks in quantum communication and computation.
However, precisely controlling complex quantum states of light in the lab remains a
challenge: current approaches are either prohibitively complex or too lossy for practical
realisation. In QuompleX, we propose an alternative approach for the control and
manipulation of quantum states of light. Recent years have seen the development of
techniques that allow unprecedented control over classical light propagation through
complex scattering media. Such media are analogous to a complex network of optical
elements, control over which has led to exciting new possibilities for biomedical imaging
and classical communication.
Here, we aim to harness the transformative potential of complex media for quantum
information processing. By carefully controlling the scattering process for multiple
photons, we will use complex media as multimode linear optical networks for
generating, manipulating, and transporting complex quantum states of light. In this
manner, we aim to overcome the problems of control and scalability that normally
plague quantum photonic networks, and push the limits of their capacity and noise-
robustness. In QuompleX, we will first theoretically study light propagation through
complex media such as multi-mode fibres and design computational algorithms for its
control and manipulation. Then, we will apply these techniques in experiment to design
high-dimensional quantum logic gates and generalised multi-mode linear networks for
generating complex, multi-photon entanglement. Finally, we will use these tools to
demonstrate multi-level, device-independent quantum communication protocols in
complex media and implement noise-resistance tests of quantum mechanics.