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Applied Physics Letters

Experimental demonstration of elastic analogues of nonseparable qutrits

M. Arif Hasan, Lázaro Calderín, Trevor D. Lata, Pierre Lucas, Keith Runge, Pierre Alix Deymier

Published Apr 20, 2020• 13 citations
Publisher

Abstract

The creation of multilevel quantum states, qudits, has revolutionized concepts for quantum computing. Classical systems that capture behavior analogous to quantum systems have been demonstrated. In this spirit, we consider a three-level classical analogue of the qudit composed of coupled acoustic waveguides. Here, we demonstrate both the experimental realization of a three-level classical analogue of the qudit and the creation and tuning of nonseparable superpositions of two of these analogues, which are classically “entangled.” Measurements of velocities and transmission inform our assignment of these nonseparable states.

DOI
10.1063/1.5145097

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The creation of multilevel quantum states, qudits, has revolutionized concepts for quantum computing. Classical systems that capture behavior analogous to quantum systems have been demonstrated. In this spirit, we consider a three-level classical analogue of the qudit composed of coupled acoustic waveguides. Here, we demonstrate both the experimental realization of a three-level classical analogue of the qudit and the creation and tuning of nonseparable superpositions of two of these analogues, which are classically “entangled.” Measurements of velocities and transmission inform our assignment of these nonseparable states.
The possibility of achieving and controlling scalable classically entangled, i.e., inseparable, multipartite states, would fundamentally challenge the advantages of quantum systems in harnessing the power of complexity in information science. Here, we investigate experimentally the extent of classical entanglement in a [Formula: see text] acoustic qubit-analogue platform. The acoustic qubit-analogue, a.k.a., logical phi-bit, results from the spectral partitioning of the nonlinear acoustic field of externally driven coupled waveguides. Each logical phi-bit is a two-level subsystem characterized by two independently measurable phases. The phi-bits are co-located within the same physical space enabling distance independent interactions. We chose a vector state representation of the [Formula: see text]-phi-bit system which lies in a [Formula: see text]-dimensional Hilbert space. The calculation of the entropy of entanglement demonstrates the possibility of achieving inseparability of the vector state and of navigating the corresponding Hilbert space. This work suggests a new direction in harnessing the complexity of classical inseparability in information science.
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.
The Controlled-NOT (CNOT) gate is the key to unlock the power of quantum computing as it is a fundamental component of a universal set of gates. We demonstrate the operation of a two-bit C-NOT quantum-like gate using classical qubit acoustic analogues, called herein logical phi-bits. The logical phi-bits are supported by an externally driven nonlinear acoustic metamaterial composed of a parallel array of three elastically coupled waveguides. A logical phi-bit has a two-state degree of freedom associated with the two independent relative phases of the acoustic wave in the three waveguides. A simple physical manipulation involving the detuning of the frequency of one of the external drivers is shown to operate on the complex vectors in the Hilbert space of pairs of logical phi-bits. This operation achieves a systematic and predictable C-NOT gate with unambiguously measurable input and output. The possibility of scaling the approach to more phi-bits is promising.
Abstract We present a model of an externally driven acoustic metamaterial constituted of a nonlinear parallel array of coupled acoustic waveguides that supports logical phi-bits, classical analogues of quantum bits (qubit). Descriptions of correlated multiple phi-bit systems emphasize the importance of representations of phi-bit and multiple phi-bit vector states within the context of their corresponding Hilbert space. Experimental data are used to demonstrate the realization of the single phi-bit Hadamard gate and the phase shift gate. A three phi-bit system is also used to illustrate the development of multiple phi-bit gates as well as a simple quantum-like algorithm. These demonstrations set the stage for the implementation of a digital quantum analogue computing platform based on acoustic metamaterial that can implement quantum-like gates and may offer promise as an efficient platform for the simulation of materials.
It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a nonseparable, tripartite GHZ-like state of path, polarization, and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols.