Quantum natural computing: from simulation to algorithms

  • Giuseppe Di Molfetta – LIS laboratory, Aix-Marseille University, Francia.

Learning goals

The aim of this course is twofold: on the one hand, to make us reflect on how computer science can provide a new language for studying nature, as differential geometry and functional analysis have been since the early 20th century. On the other hand, cellular automata as models and simulators, become at the same time platforms for experimenting with new protocols and quantum algorithms inspired by physical phenomena. Both aspects will be studied through higher levels of complexity, starting from the basics and arriving on the last day at a broader look at the challenges and problems currently open.

Program

A modern and gentle introduction to quantum theory. Quantum walk and their generalization Quantum celullar automata. Simulating physics I and II. Natural-inspired algorithms and distributed architectures.

Bibliography

Quantum Computation and Quantum Information (Nielsen, Chuang), Cambridge

Quantum Information Theory (Wilde), Cambridge

Lecture Notes on Quantum Algorithms (Childs)

A review of Quantum Cellular Automata (Farrelly)

Di Molfetta, Giuseppe, Marc Brachet, and Fabrice Debbasch. «Quantum walks as massless Dirac fermions in curved space-time.» Physical Review A 88.4 (2013): 042301.

Manighalam, Michael, and Giuseppe Di Molfetta. «Continuous Time Limit of the DTQW in 2D+ 1 and Plasticity.» Quantum Information Processing 20.2 (2021): 1-24.

Roget, M., Guillet, S., Arrighi, P., Di Molfetta, G. (2020). Grover search as a naturally occurring phenomenon. Physical Review Letters, 124(18), 180501.

Succi, Sauro, Fran ̧cois Fillion-Gourdeau, and Silvia Palpacelli. «Quantum lattice Boltzmann is a quantum walk.» EPJ Quantum Technology 2.1 (2015): 1-17.

Hatifi, M., Di Molfetta, G., Debbasch, F., Brachet, M. (2019). Quantum walk hydrodynamics. Scientific reports, 9(1), 1-7.

Previous requirements

Good understanding of standard linear algebra (at basic universitary level). If not met it’s still possible to present most topics under a more ’graphical’ point of view. The content is globally self-consistent, no need of previous knowledge in physics or theoretical computer science.

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