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arXiv:2304.03655

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 Apr 7, 2023• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2304.03655

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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.
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.
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.
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.
One of the main challenges in quantum computing is implementing algorithms within quantum optical free-space and integrated circuits. This research focuses on the quantum addition algorithm, derived from the Deutsch-Jozsa algorithm, to advance quantum computing using optical technologies. The developed quantum optical integrated circuit is built on a hybrid substrate with interconnected components on a silicon dioxide base. Qubits and their states are arranged according to the requirements of each quantum algorithm. In the Fourier transform section, qubits act as propagation modes within silicon waveguides, with emitted photons representing the Fourier transform after traveling a distance of π/2. The phase-shifting section consists of two parts: one shifts the phase of incoming photons by π, while the other modulates this shift based on the quantum full adder algorithm. The first employs a photonic crystal for short phase shifts, which are adjusted via impurities in the silicon substrate and controlled by an electro-optic circuit. Additionally, single-mode waveguides made of silicon dioxide and air serve as qubits. By coupling photon amplitudes, a comparator circuit is triggered based on the generated output. Through these integrations, the sum of two quantum numbers can be represented at the output. This underscores the importance of designing and simulating a full adder within quantum optical integrated circuits to address the complexities inherent in quantum computing.
Quantum Machine Learning (QML) is rapidly emerging as a transformative paradigm for various computational tasks, including machine learning. Traditional machine learning algorithms often struggle with high-dimensional data and complex non-linear relationships, limiting their effectiveness in certain applications. This paper proposes a novel quantum machine learning optimization algorithm, dubbed the "Quantum-Enhanced Gradient Descent" (QED) algorithm, designed to address these challenges. We explore the potential of quantum computing to accelerate gradient descent and enhance the exploration of solution spaces, ultimately leading to improved model performance. The core mechanism involves leveraging quantum properties to perform more efficient and nuanced parameter adjustments, specifically focusing on non-linear optimization. This paper provides a detailed theoretical foundation and preliminary experimental validation demonstrating the effectiveness of QED in optimizing machine learning models, particularly concerning high-dimensional data and complex non-linear dependencies.