Testing Quantumness: From Artificial Quantum Arrays to Lattice Spin Models and Spin Liquids

Quantum mechanics is one of the best-confirmed theories in physics. Over the last two decades of steady and spectacular improvements in experimental techniques, there were no indications that quantum mechanics fails even when describing macroscopic systems.

We are now at the beginning of a "second quantum revolution'', where significant research efforts are being shifted from understanding quantum mechanical systems to applying essentially quantum properties of macroscopic systems in order to develop new quantum technologies (e.g., in quantum computing).

However, direct simulation of large enough systems with quantum mechanical behaviour is practically impossible, because of the astronomical computational resources it requires. Current developments in quantum engineering already brought us to face this barrier. It is therefore necessary to develop a set of approximate approaches, which are nonetheless precise enough, at least on average, to provide the understanding of and a guidance to the development of still larger artificial quantum systems, to the benefit of both fundamental science and cutting edge technology. In addition, magnetic materials, behaving quantum mechanically, require the same treatment with respect to their "quantumness", in this case in the thermodynamic limit. The goal of this project is to develop such a general theory and apply it to a number of important problems.

The results of this research proposal will have significant impact on both the academic scientific community (e.g., quantum information and computing, quantum materials and metamaterials, cold atom and trapped ion systems, magnetism) as well as on the research and development sector of the emerging quantum information and quantum technology industry.
Recent developments in experimental techniques allow nowadays the realisation of quantum devices comprised of thousands of unit elements ("artificial atoms", such as superconducting quantum bits - or natural systems, such as electron or nuclear spins) and control and maintain them in at least a partially quantum coherent state for finite periods of time. These possibilities bring promise of both new technologies and better understanding of fundamental physics, but it cannot be realised without a proper theoretical underpinning. Unfortunately, the existing theoretical methods are inadequate to the task.
We expect that our results will benefit fundamental science through the development of new theoretical tools capable of bridging the computational capacity gap. The looming impossibility to predict the behaviour of any large enough quantum devices (e.g., quantum metamaterials; adiabatic or gate-based quantum processors, etc.), and even to test their "quantumness'' using classical tools, is constraining further progress in the field. Taking the optimistic view that quantum computing is not fundamentally restricted (by, e.g., limits on the size of systems capable of demonstrating quantum behaviour), it is realistic to expect, based on the current state of the art, that a quantum processor capable of simulated such devices, including itself, accurately and quickly enough to be useful, will contain significantly more physical qubits than the current record of approx. 500 in a D-Wave quantum annealer. Therefore, we cannot avoid the need to simulate the behaviour of large, essentially quantum systems by classical means.
We will also provide a theoretical description, design and simulation of model quantum coherent systems, such as quantum metamaterials (QMM), quantum metamaterial-based detectors and quantum communications devices. These may include QMM-based devices for quantum communications in the microwave range; quantum-limited medical imaging devices; QMM-based quantum repeaters, etc. This project will contribute to laying the foundation for the development of quantum engineering, i.e., the development of macroscopic quantum coherent structures built from artificial, controllable quantum unit blocks.
The potential technological impact of this project will be primarily in the field of quantum sensing, imaging, measurement and communication, with such applications as quantum detectors, repeaters and optical elements. Significant influence on quantum computing is also highly probable, e.g., from efficient simulation of extended quantum structures to new ways for their optimisation. We will pay special attention to the identification, protection and exploitation of the IP generated in the projects, since this area of technology is one where major breakthroughs are likely to happen. The success of this project will provide a major boost to the UK expertise in this crucial area and will help to compete with the North American and Japanese R&D effort.
Finally, potential societal benefits will come from the results of our proposal through broader dissemination. We shall use public lectures and other outreach activities (e.g., the Quantum Cambridge initiative described in the Track Record) to communicate our results to the public and make them aware of the potential as well as the limitations of new quantum technologies. We will also endeavour to engage policy makers by inviting them to some of the more high-profile outreach events and by private discussion.
Societal, academic and industrial benefits will indirectly derive from the training of young scientists.