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Optics Express

Emulating the Deutsch-Josza algorithm with an inverse-designed terahertz gradient-index lens

Ashley N. Blackwell, Riad Yahiaoui, Yi-Huan Chen, Pai‐Yen Chen, Thomas A. Searles, Zizwe Chase

Published Aug 4, 2023• 2 citations
Publisher

Abstract

An all-dielectric photonic metastructure is investigated for application as a quantum algorithm emulator (QAE) in the terahertz frequency regime; specifically, we show implementation of the Deustsh-Josza algorithm. The design for the QAE consists of a gradient-index (GRIN) lens as the Fourier transform subblock and patterned silicon as the oracle subblock. First, we detail optimization of the GRIN lens through numerical analysis. Then, we employed inverse design through a machine learning approach to further optimize the structural geometry. Through this optimization, we enhance the interaction of the incident light with the metamaterial via spectral improvements of the outgoing wave.

DOI
10.1364/oe.495919

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An all-dielectric photonic metastructure is investigated for application as a quantum algorithm emulator (QAE) in the terahertz frequency regime; specifically, we show implementation of the Deustsh-Josza algorithm. The design for the QAE consists of a gradient-index (GRIN) lens as the Fourier transform subblock and patterned silicon as the oracle subblock. First, we detail optimization of the GRIN lens through numerical analysis. Then, we employed inverse design through a machine learning approach to further optimize the structural geometry. Through this optimization, we enhance the interaction of the incident light with the metamaterial via spectral improvements of the outgoing wave.
Photonic systems utilized as components for optical computing promise the potential of enhanced computational ability over current computer architectures. Here, an all-dielectric photonic metastructure is investigated for application as a quantum algorithm emulator (QAE) in the terahertz frequency regime; specifically, we show implementation of the Deustsh-Josza algorithm. The design for the QAE consists of a gradient-index (GRIN) lens as the Fourier transform subblock and silicon as the oracle subblock. First, we detail optimization of the metastructure through numerical analysis. Then, we employed inverse design through a machine learning approach to further optimize the structural geometry. In particular, we improved the lens thickness, in order to enhance the resulting output signal for both balanced and constant functions. We show that by optimizing the thickness of the gradient-index lens through ML, we enhance the interaction of the incident light with the metamaterial leading to a stronger focus of the outgoing wave resulting in more accurate implementation of the desired quantum algorithm in the terahertz.
During the past few years, a lot of efforts have been devoted in studying optical analog computing with artificial structures. Up to now, much of them are primarily focused on classical mathematical operations. How to use artificial structures to simulate quantum algorithm is still to be explored. In this work, an all-dielectric metamaterial-based model is proposed and realized to demonstrate the quantum Deutsch-Jozsa algorithm. The model is comprised of two cascaded functional metamaterial subblocks. The oracle subblock encodes the detecting functions (constant or balanced), onto the phase distribution of the incident wave. Then, the original Hadamard transformation is performed with a graded-index subblock. Both the numerical and experimental results indicate that the proposed metamaterials are able to simulate the Deutsch-Jozsa problem with one round operation and a single measurement of the output eletric field, where the zero (maximum) intensity at the central position results from the destructive (constructive) interference accompanying with the balance (constant) function marked by the oracle subblock. The proposed computational metamaterial is miniaturized and easy-integration for potential applications in communication, wave-based analog computing, and signal processing systems.
Metamaterials, artificially structured electromagnetic (EM) materials, have enabled the realization of many unconventional EM properties not found in nature, such as negative refractive index, magnetic response, invisibility cloaking, and so on. Based on these man-made materials with novel EM properties, various devices are designed and realized. However, quantum analog devices based on metamaterials have not been achieved so far. Here, metamaterials are designed and printed to perform quantum search algorithm. The structures, comprising of an array of 2D subwavelength air holes with different radii perforated on the dielectric layer, are fabricated using a 3D-printing technique. When an incident wave enters in the designed metamaterials, the profile of beam wavefront is processed iteratively as it propagates through the metamaterial periodically. After ≈N roundtrips, precisely the same as the efficiency of quantum search algorithm, searched items will be found with the incident wave all focusing on the marked positions. Such a metamaterial-based quantum searching simulator may lead to remarkable achievements in wave-based signal processors.
In this Letter, we construct a metamaterial with dual-mode electromagnetically induced transparency (EIT)-like behavior by introducing "bright atoms," "quasi-dark atoms," and "dark atoms" simultaneously. The dual-mode EIT-like behavior has been demonstrated both experimentally and theoretically in terahertz (THz) regime. At two EIT-like modes, slow light is also observed as two time-delayed wave packets, and the effective group refractive index can reach 10(2). Furthermore, stable dual-mode EIT-like behavior is verified in this metamaterial for a wide range of oblique incident angles. Our work provides a design approach to mimic dual-mode EIT, and such an approach may achieve potential applications on miniaturized and versatile THz devices.
Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.