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

Paper Number: 150081

150081 - Operations With a Mechanical Platform: Acoustic Analogues of Qubits 

Introduction

I present the theoretical framework and experimental realization of permutations, including CNOT and SWAP, using logical phi-bits. These classical analogues of qubits are nonlinear acoustic modes supported by externally driven acoustic metamaterials. Permutation is an essential concept for many algorithms in sectors such as cryptography, analysis, and statistics. Permutations become increasingly difficult in digital computers as dataset size increases due to computation time. Quantum computers offer a possible solution as they have unique parallel computing abilities. However, current quantum computing technology still struggles with multi-qubit superposition fragility and weak correlation that limits how many qubits can be manipulated at once. This leads to permutations relying on circuits of single and double qubit gates. Using logical phi-bits I demonstrate all possible permutations in a two logical phi-bit system as well as a scalable permutation that works for any number of logical phi-bits. Using logical phi-bits, I can complete each permutation with a single physical action compared to the many physical actions with a quantum computer.

Contribution

These logical phi-bits enabled by a mechanical system provide an efficient and stable analogy to quantum computing. Logical phi-bits avoid quantum fragility inherent in qubits. At any time, the phase of the logical phi-bit can be measured without worry of a collapsing waveform. As it is mechanical, it operates at room temperature, as opposed to the cryogenic temperatures required for quantum computers. This mechanical platform also brings a unique take on quantum computing where instead of completing operations through a series of gates in a circuit, operations are completed in a single step of changing the driver input.

Methodology

The mechanical system consists of three aluminum waveguides in a parallel array coupled with epoxy. Using ultrasonic transducers driven by two separate signal generators, the first and second waveguides are excited initially with driving frequencies of 62 and 66 kHz respectively. The frequency in the first waveguide is then swept from 62 to 66 kHz. Using another set of transducers at the opposite ends of the waveguides, the amplitude and phase of the propagated waves is measured, and fast Fourier transformed. The amplitudes of the transformed waves are analyzed in the frequency domain where peaks corresponding to nonlinear modes can be observed at linear combinations of the two driving frequencies.

These nonlinear modes give rise to phi-bits and can be characterized by their unique combination of the two driving frequencies. Phi-bits can also be characterized by their phase difference between either the first and second or the first and third waveguides. These phase differences are controlled by varying the frequency in waveguide 1 and they exhibit continuous behavior as well as behavior where the phase difference jumps by  jump behavior.

To complete these permutations, I also introduce a representation based on the Bloch sphere that utilizes the Heaviside function to enable a single representation for all two phi-bit permutations.

Results and Conclusions

Using this representation, I can create a four-element initial state vector and permute it in any possible way by changing the driving frequency of the first waveguide. This includes a CNOT gate as well as a SWAP gate. I also present a scalable permutation that inverts a state vector of any size with a single physical action. This permutation is experimentally demonstrated with two and three phi-bits but can be accomplished with any number of phi-bits. This permutation demonstrates the exponential advantage as for a system of 50 phi-bits, the permutation would be able to invert  or approximately  elements with the same action used to permute 4 elements. These permutations would all require multiple physical actions in a quantum computer but require only a single frequency change in this mechanical system.

With this research I demonstrate a significant step towards quantum computing analogues as an efficient way to perform permutations through topological acoustics.

 

Presenting Author: David Cavalluzzi University of Arizona

Presenting Author Biography: David is an undergraduate student in the Department of Electrical and Computer engineering at the University of Arizona, working with Dr. Pierre Deymier on mechanical analogues of quantum bits.

Authors:

David Cavalluzzi University of Arizona
Akinsanmi Ige University of Arizona
Keith Runge University of Arizona
Pierre Deymier University of Arizona