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SUMMARY:TOWARDS QUANTUM COMPUTATIONAL MECHANICS - Dr Burigede Liu\, CUED
DTSTART:20240503T150000Z
DTEND:20240503T160000Z
UID:TALK213322@talks.cam.ac.uk
CONTACT:46601
DESCRIPTION:The advent of quantum computers\, operating on entirely differ
 ent physical principles and abstractions from those of\nclassical digital 
 computers\, sets forth a new computing paradigm that can potentially resul
 t in game-changing efficiencies and computational performance. Specificall
 y\, the ability to simultaneously evolve the state of an entire quantum sy
 stem leads to quantum parallelism and interference. Despite these prospect
 s\, opportunities to bring quantum computing to bear on problems of comput
 ational mechanics remain largely unexplored. In this work\, we demonstrate
  how quantum computing can indeed be used to solve representative volume e
 lement (RVE) problems in computational homogenisation with polylogarithmic
  complexity of O((log N) c )\, compared to O(N c ) in classical computing.
  Thus\, our quantum RVE solver attains exponential acceleration with respe
 ct to classical solvers\, thus bringing concurrent multiscale computing cl
 oser to practicality. The proposed quantum RVE solver combines conventiona
 l algorithms such as a fixed-point iteration for a homogeneous reference m
 aterial and the Fast Fourier\nTransform (FFT). However\, the quantum compu
 ting reformulation of these algorithms requires a fundamental paradigm shi
 ft and\na complete rethinking and overhaul of the classical implementation
 . We employ or develop several techniques\, including the Quantum Fourier 
 Transform (QFT)\, quantum encoding of polynomials\, classical piecewise Ch
 ebyshev approximation of functions and an auxiliary algorithm for implemen
 ting the fixed-point iteration and show that\, indeed\, an efficient imple
 mentation of RVE solvers on quantum computers is possible. We additionally
  provide theoretical proofs and numerical evidence confirming the\nanticip
 ated O ((logN) c ) complexity of the proposed solver.
LOCATION:JDB Seminar Room\, CUED
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