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International Conference on Industrial Engineering and Operations Management (IEOM)

Decoherence-Resistant Elastic Bits: A Novel Approach to Quantum Analogue Computing Using Coherent Superpositions of States

Kazi Tahsin Mahmood, M. Arif Hasan

Published Oct 10, 2023• 0 citations
Publisher

Abstract

In quantum information science and technology (QIST), the superposition of states is pivotal. Current qubits, formed by superposing two pure states, are foundational in QIST but are susceptible to decoherence, causing loss of superposed states. Addressing this, we introduced an "elastic bit" using the Hertz-type nonlinearity of elastic beads under external driving. These beads exhibit phase-dependent nonlinear vibrations, leading to coherent superpositions of energy states in linear vibration modes. The resulting amplitudes span a two-dimensional Hilbert space, with time allowing parametric spanning. We showcased the Hadamard gate, translating one state superposition to another through a unitary transformation. Remarkably, these elastic bits operate at room temperature and resist decoherence, making them apt for intermediate-scale quantum analogue computing. They offer solutions for challenges in supercomputing for artificial intelligence and autonomous vehicle data processing.

DOI
10.46254/ev01.20230102

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In quantum information science and technology (QIST), the superposition of states is pivotal. Current qubits, formed by superposing two pure states, are foundational in QIST but are susceptible to decoherence, causing loss of superposed states. Addressing this, we introduced an "elastic bit" using the Hertz-type nonlinearity of elastic beads under external driving. These beads exhibit phase-dependent nonlinear vibrations, leading to coherent superpositions of energy states in linear vibration modes. The resulting amplitudes span a two-dimensional Hilbert space, with time allowing parametric spanning. We showcased the Hadamard gate, translating one state superposition to another through a unitary transformation. Remarkably, these elastic bits operate at room temperature and resist decoherence, making them apt for intermediate-scale quantum analogue computing. They offer solutions for challenges in supercomputing for artificial intelligence and autonomous vehicle data processing.
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One of the quantum theory concepts on which quantum information processing stands is superposition. Here we provide experimental evidence for the existence of classical analogues to the coherent superposition of energy states, which is made possible by the Hertz-type nonlinearity of the granules together with the external driving field. The granules' nonlinear vibrations are projected into the linear modes of vibration, which depend on one another through the phase and form a coherent superposition. We show that the amplitudes of the coherent states form the components of a state vector that spans a two-dimensional Hilbert space, and time enables the system to span its Hilbert space parametrically. Thus, the superposition of states can be exploited in two-state quantum-like computations without decoherence and wave function collapse. Finally, we demonstrate the experimental realization of applying a reversible Hadamard gate to a pure base state that brings the state into a superposition.
Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.
Now there is a great interest in the field of information technologies cause development a quantum computer that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Qubit - is a unit of quantum information—the quantum analogue of the classical bit. As a bit, a qubit admits two of its own state, but it can be in superposition. Following the development of a quantum computer will need to establish a standard unit of quantum information. The search for a candidate for the role of the qubit (and, stable) can give perspectives to the development of quantum metrology.
Quantum computing, fuelled by the extraordinary properties of quantum bits (qubits) – superposition and entanglement, is on the cusp of a technological revolution. Superposition allows qubits to exist in multiple states simultaneously, accelerating problem-solving in cryptography, drug discovery, optimization, material science, and artificial intelligence. Quantum algorithms like Shor's and Grover's are poised to disrupt classical encryption and transform data analysis. Entanglement, a mysterious quantum connection, enhances quantum communication and error correction, while offering secure quantum teleportation. However, quantum computing faces critical challenges such as qubit stability, scaling, error correction, and quantum software development. As quantum technology advances, it promises to reshape industries and society, addressing challenges in fields like climate modelling, energy, finance, and logistics. The path forward requires collaboration, ethical considerations, and a commitment to responsible development. In this quantum era, the future is quantum, promising innovation, security, and transformative computational power.
Computers have transformed the way we live, work, and innovate. While Quantum computers based on quantum bits (qubits) exploit principles such as superposition and entanglement to offer unprecedented computational power compared to conventional computers. However, their scalability and practical realization are limited by challenges associated with wavefunction decoherence, the need for cryogenic temperatures, and extreme sensitivity to noise and environmental disturbances. The analogy between topological acoustic waves and quantum mechanics offers a path toward the design and operation of an acoustic quantum-analogue computer which does not suffer from the fragility of qubits. In this work, we present the demonstration and characterization of such a scalable, cost-effective, room-temperature acoustic analogue quantum computing platform. This platform harnesses the intrinsic nonlinearity of physical systems to generate wave superposition. We demonstrate several scalable quantum operations, including the realization of quantum permutation gates and quantum-inspired cryptography, using experimental results from this system. In addition, we discuss the underlying concepts and characterization of the platform, along with the ongoing efforts both through analytical simulation in ANSYS mechanical and experimental validation to develop a model of the acoustic quantum analogue computer. Finally, the dissertation concludes with an assessment of the platform’s reliability and robustness, highlighting its promise as a practical alternative for quantum-inspired computation.