Leveraging a Discrete-Time-Crystal to Solve Classification Problems with a Quantum Extreme Learning Machine

Abstract

This thesis explores the field of Quantum Extreme Learning Machines based on manybody localized discrete time crystals. This approach holds two advantages: Leveraging an exponentially large Hilbert states while not relying on error-corrected quantum gates. Firstly, the concept of discrete time crystals and the theoretical framework behind QELMs are presented. After some introductory results to test the potentials and limitations of unitary evolution, the method’s phase dependency is discussed to observe the melting of the discrete time crystal also in the classification accuracies. The remainder of the thesis can be split into two categories: Investigating effects on the classification accuracies when changing the quantum layer and an investigation of amendments in the readout layer. Both parts contain a comparison for thermal and discrete time crystal phase as well as reasonable comparisons with classical results. In the readout layer analysis new readout methods are presented that hold the potential of increasing the classification accuracies based on random shuffling. The work concludes with a combination of all methods and an evaluation of their combined performance. Overall, the thesis provides a comprehensive overview of the exciting field of Quantum Extreme Learning Machines, offering new insights as well as new pathways for further advancements in the field.