Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 150444

150444 - Quantum Realm in Classical Mechanics: A New Basis of Topological Computing 

In the realm of quantum information and science, the classical analogous mechanics is creating a new wave of research for information processing. Through a classical granular network, we form a classical counterpart of quantum bit (qubit), an elastic bit, which is necessary to understand the states of quantum mechanics. We form the elastic bit using Hertz-type contact granular beads, where the single point contact between the beads makes the system highly adaptable to external excitation. The tuning of the frequency and amplitude of the external driver and the static precompression on the beads can make the system from highly to weakly nonlinear and even linearized. With these, we control the elastic bit's formation through the displacement field's orthonormal vector. The orthonormal basis gives us the coefficient of the complex amplitudes, which creates the superposition of states and forms dynamic and phase-dependent movements. This phenomenon demonstrates the energy levels of the quantum superposition, which are governed by the phase correlation between in-phase and out-of-phase motion. The linearized system shows time-independent superposition of states, but nonlinearity allows time to change the superposition of states in parametric space. The linearized superposition of states shows the evolution in a plane in the Bloch states, but nonlinearity shows the evolution in all the regions. We understand the relationship between the quantum and classical systems using the accumulation of the Berry phase. We both analytically and experimentally show the accumulation of trivial and nontrivial Berry phases and the relation of the system's dynamics with the superposition of states. To validate the quantum realm in the classical system, we apply the quantum analogous gate to show the states' evolution without changing the external excitations. This study helps understand topological computing, as when the elastic bits are wrapped around each other, the system undergoes a unitary transformation that can be used to perform quantum gates. The exchange of elastic bits produces a specific Berry phase that depends on the path chosen during the exchange, resulting in nontrivial braiding. This investigation also applies to non-Holonomic computing, as the dynamics depend on the non-integrable constraints leading to path-dependent constraints. The elastic bits and Berry phase demonstrate the Majorana encoding as it shares the mode non-locally. The Berry phase makes a system susceptible to disturbance, making our classical system decoherence-free and having no issue with the wave function collapse. This investigation of berry phases via elastic bit manipulation paves the way for data processing and computations inspired by quantum mechanics.

[Funding: NSF grant # 2204382, 2242925]

Presenting Author: Kazi Tahsin Mahmood Wayne State University

Presenting Author Biography: Kazi Tahsin Mahmood is a graduate student in the Department of Mechanical Engineering at Wayne State University. He earned his B.Sc. in Mechanical Engineering from Bangladesh University of Engineering and Technology. His undergraduate research field is on Mechanics of Materials. He is currently working on the topological characteristics of nonlinear granular beads and studying the classical analogous superposition of states. His research spans both the theoretical and experimental aspects, particularly focusing on the harmonic oscillations exhibited by these beads in nonlinear systems.

Authors:

Kazi Tahsin Mahmood Wayne State University
M. Arif Hasan Wayne State University