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.
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.
Owing to the inherent advantages of parallelism, rapid processing speed, and minimal energy consumption, optical analog computing has witnessed a progressive development. Quantum optical computing exceeds the capabilities of classical computing in terms of computational speed in numerous tasks. However, existing metamaterial-based quantum Deutsch-Jozsa (DJ) algorithm devices have large structural dimensions and are not suitable for miniaturized optical computing systems. Furthermore, most reported on-chip metasurface devices, rendered monofunctional after fabrication, do not possess sophisticated optical systems. In this work, we develop an electrically tunable on-chip DJ algorithm device on a lithium-niobate-on-insulator (LNOI) platform. The on-chip device consists of various etched slots, each with carefully designed size. By applying different external voltages to each individual unit, precise phase redistribution across the device is attainable, enabling the realization of tunable DJ algorithm. Notably, we can determine whether the oracle metasurface yields a constant or balance function by measuring the output electric field. The on-chip device is miniaturized and easy to integrate while enabling functional reconfiguration, which paves the way for numerous applications in optical computing.
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.
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.
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.
Abstract This laboratory work presents a practical implementation of the Deutsch–Jozsa algorithm using the Qiskit framework, complemented by the application of artificial intelligence tools such as GPT-based systems to assist in circuit design, debugging, and conceptual analysis. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and aims to bridge theoretical quantum algorithms with executable quantum programs. In Laboratory Work No. 6, participants construct the Deutsch–Jozsa algorithm for n=4n = 4n=4 input qubits within an oracle-based computational model. The circuit includes a quantum register qqq representing the oracle input qubits, an output qubit outoutout, and a classical register ccc for measurement results. The algorithm begins by applying Hadamard (H) gates to all oracle qubits to create a uniform superposition over the input space. The output qubit is prepared using Pauli-X (X) and Hadamard (H) gates to establish the appropriate phase kickback configuration. A visual barrier is introduced in the circuit to clearly separate initialization, oracle evaluation, and interference stages. After the oracle operation, a second layer of Hadamard gates is applied to the input qubits, followed by measurement into classical bits. The resulting measurement pattern allows deterministic distinction between constant and balanced Boolean functions with a single oracle query—demonstrating exponential speedup compared to classical deterministic algorithms. The laboratory exercise emphasizes structured circuit design, oracle modeling, phase interference analysis, and measurement interpretation. Additionally, GPT-based AI tools are used to support code generation, algorithm explanation, and optimization, illustrating how modern artificial intelligence systems can enhance quantum programming workflows. Through simulation and execution on cloud-based quantum hardware, participants gain both theoretical insight and practical experience with one of the foundational quantum algorithms and its implementation in contemporary quantum computing ecosystems.