Quantum-Elastic Geometry: From Geometric Extension to Linear and Non Linear Regimes

Ricardo Alejandro Troncoso Perez, Cristian Andres Martinez Silva

Jérémie Boulanger, Nicolas Le Bihan, Stéfan Catheline +1 more

We report the experimental observation ofageometricphase for elastic wavesin awaveguidewith helicalshape. Thesetup reproducestheexperimentbyTomita and Chiao (Phys. Rev. Lett. 57, 1986) that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of non-adiabatic geometric has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix ’ radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase. 1.

Jincheng Zhang

This paper explores the potential of non-linear geometric structures to enhance quantum algorithm efficiency. Traditional quantum algorithms often focus on classical computation, but this work proposes a novel approach that leverages non-linear properties to achieve significant performance gains. We outline a new quantum algorithm framework specifically designed to address challenges within non-linear geometric contexts, demonstrating increased efficiency through a unique approach to quantum computation. The core mechanism centers on a modified quantum circuit that intrinsically responds to non-linearities.

André Lichnerowicz

James Thomas Wheeler

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, exhibits correlations that defy classical intuition. While entanglement has been extensively studied in the realm of quantum information theory, its practical applications remain limited by inherent fragility. This research investigates a novel approach to stabilizing entangled states through a non-linear geometry mapping technique. We propose a method to precisely manipulate the features of entangled states by mapping them onto a tailored geometric space, thereby enhancing their resilience against decoherence. This work leverages the unique properties of quantum geometry, specifically the non-linear nature of spacetime, to achieve a significant improvement in entanglement stability. The core mechanism centers around the creation of a specific geometric structure that inherently mitigates the degradation associated with entanglement. This research offers a promising pathway towards harnessing the full potential of quantum entanglement in complex systems.