Minisymposium (ID: SS-QEHA)

Quantum Engineering meets Harmonic Analysis

Bing-Zhao Li (School of Mathematics, Beijing institute of Technology), Artur Sowa (Department of Mathematic and Statistics, University of Saskatchewan), Alexandre Zagoskin (Department of Physics, Loughborough University)

Developments in design, fabrication and control of artificial quantum-coherent devices hold a promise of novel technologies based on utilisation of subtle quantum effects, such as entanglement, superposition, and nonlocality. This should enable not just quantum computing and communications, but a whole range of breakthrough capabilities, such as ultra-sensitive signal detection, ultra-resolved and fast scientific and medical imaging, all outside the reach for the technologies that we have known till now.

One of the main obstacles to rapid progress is the ineffectiveness of the classical computational approach to the modelling of large-scale quantum coherent structures, especially in such cases when quantum correlations on all scales must be accounted for. This is a fundamental problem stemming from the (generally) exponential growth of complexity with scale. At the same time, a number of special cases of complex quantum systems are known to be explicitly analyzable/solvable. In those instances, progress was achieved via the use of Harmonic Analysis. Examples include the analysis of spin systems (via the Fourier methods) going back to 1970s, or the analysis of large molecules (via the Repeat Space Theory and Toeplitz operators) in the 1990s and 2000s. More recently, it has been demonstrated that the Haar wavelet transform helps obtain a solvable model of a certain type of optical quantum-metamaterial. Such special cases help glean invaluable insights into the nature of general quantum-coherent structures.

It is therefore likely that a systematic dialogue between the camps of Quantum Engineering and Harmonic Analysis will stimulate progress in the modelling of large quantum coherent structures. This is precisely the main objective of our session. We welcome contributions from mathematicians, physicists, engineers, and computer scientists that aim to bring the two streams of research closer together. Examples of relevant themes include the Fractional and Canonical Linear Operator Transforms, the Wigner-Weyl transform, innovative methods in Signal Processing, including quantum Signal Processing, innovative approaches to the MRI and NMR imaging, semi-classical methods in quantum system modelling, quantum-field-theoretic analysis of coherent structures, Quantum Optics, quantum applications of Wavelet Theory, and Multiscale Methods in Quantum Physics. We also invite contributions on experimental design and implementation of quantum coherent devices (at either component- or system-level).

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