{"id":23423,"date":"2024-12-15T22:18:14","date_gmt":"2024-12-15T15:18:14","guid":{"rendered":"https:\/\/stei.itb.ac.id\/?page_id=23423"},"modified":"2024-12-15T22:23:42","modified_gmt":"2024-12-15T15:23:42","slug":"poster6","status":"publish","type":"page","link":"https:\/\/stei.itb.ac.id\/en\/poster6\/","title":{"rendered":"Finding Hadamard Matrices using QAOA Algorithm"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid kepala vc_custom_1734236300248 vc_row-has-fill\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"container\" ><div class=\"vc_row wpb_row vc_inner vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\"><div class=\"vc_btn3-container vc_btn3-inline vc_do_btn\" ><button class=\"vc_general vc_btn3 vc_btn3-size-lg vc_btn3-shape-rounded vc_btn3-style-modern vc_btn3-icon-left vc_btn3-color-white\" onclick=\"history.back()\"><i class=\"vc_btn3-icon fas fa-home\"><\/i> Kembali ke Beranda<\/button><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734170418007\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Prof. Andriyan Bayu Suksmono, PhD.<\/strong><br \/>\nSchool of Electrical Engineering and Informatics<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734168902943\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h5><strong>Abstract<\/strong><\/h5>\n<p>Finding Hadamard matrices is a computationally intensive problem due to the exponential growth of possible binary matrix configurations. This study explores a qubit-efficient method using Quantum Approximate Optimization Algorithm (QAOA) on universal quantum computers, bypassing the ancillary qubit needs of quantum annealers. Experiments demonstrate the ability to construct Williamson and Baumert-Hall Hadamard matrices of orders up to 132 with exponential performance improvement over random algorithms.<\/p>\n<p>Keyword:QuantumSupremacy,QuantumUtility,MatriksHadamard,QAOA<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734275402962 vc_row-o-content-top vc_row-flex\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h5><strong>Introduction<\/strong><\/h5>\n<p>Hadamard matrices are orthogonal binary matrices with applications in communication systems, signal processing, and error correction. While low-order matrices can be constructed using classical methods, finding higher-order matrices is computationally intensive. The problem becomes infeasible for classical computing due to the exponential growth of orthogonality tests.<\/p>\n<p>Quantum computing offers new possibilities for addressing such hard optimization problems. Quantum annealers have successfully found some high-order Hadamard matrices but require additional ancillary qubits, making scalability a challenge. This motivates the exploration of gate-based quantum computing, which eliminates ancillary qubit needs for multi-body interactions.<\/p>\n<p>This paper investigates the use of QAOA for constructing Hadamard matrices on universal quantum computers. By employing QAOA, the computational complexity is significantly reduced, enabling the construction of large- order matrices. The research aims to demonstrate the feasibility and advantages of this approach compared to classical and quantum annealing methods.<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div  class=\"wpb_single_image wpb_content_element vc_align_center wpb_content_element vc_custom_1734275232574\">\n\t\t\n\t\t<figure class=\"wpb_wrapper vc_figure\">\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"887\" height=\"453\" src=\"https:\/\/stei.itb.ac.id\/wp-content\/uploads\/6.-Riset-GB-Prof.jpg\" class=\"vc_single_image-img attachment-full\" alt=\"\" title=\"6. Riset GB - Prof\" \/><\/div><figcaption class=\"vc_figure-caption\">Figure 1. Block Diagram of The Experiment<\/figcaption>\n\t\t<\/figure>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734236752660 vc_row-o-content-top vc_row-flex\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h5><strong>Research Method<\/strong><\/h5>\n<p><strong>Williamson and Baumert-Hall Methods<\/strong><br \/>\nTo reduce variable growth, the Williamson and Baumert-Hall methods decompose the problem into submatrices with complexity O(M), where M is the matrix order. These methods enable efficient matrix construction, avoiding the O(M^2) scaling of direct searches.<\/p>\n<p><strong>QAOA Framework<\/strong><br \/>\nQAOA is based on a hybrid quantum-classical approach, where a problem Hamiltonian and a mixer Hamiltonian guide qubits to optimal configurations. The algorithm iteratively adjusts circuit parameters to minimize the cost function using classical optimizers.<\/p>\n<p><strong>Quantum Circuit Construction<\/strong><br \/>\nQuantum circuits for 1- to 4-body interactions are designed using combinations of Z-rotation and CNOT gates. The circuits are implemented on IBM&#8217;s quantum simulator, capable of simulating up to 32 qubits. Cascaded circuit designs enable scalability for high-order problems.<\/p>\n<p><strong>Performance Metrics<\/strong><br \/>\nThe efficiency of QAOA is evaluated using the Quantum-to-Random Algorithm Ratio (QRAR), which compares the success rate of QAOA to that of a random search. Higher QRAR values indicate better algorithmic performance.<\/p>\n<p><strong>Experiment Setup<\/strong><br \/>\nExperiments were conducted to construct Hadamard matrices of orders 44 and 132 using Williamson and Baumert-Hall methods. Simulations explored the impact of increasing circuit layers and qubit counts on performance, with optimizations performed using COBYLA. Figure 1 shows the experiment setup.<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734169842459\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h5><strong>Discussion &amp; Result<\/strong><\/h5>\n<p>Experiments successfully identified Williamson Hadamard matrices of order 44 and Baumert- Hall matrices of order 132. The latter one is shown in Fig.2. The QAOA algorithm demonstrated exponential improvements in efficiency compared to random algorithms, with QRAR values approaching theoretical maxima.<\/p>\n<p>Scalability was validated for problems with up to 24 qubits, showing consistent performance gains with increasing circuit layers. However, noise and complexity in higher-order searches revealed the need for improved quantum error mitigation techniques..<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div  class=\"wpb_single_image wpb_content_element vc_align_center wpb_content_element vc_custom_1734275714138\">\n\t\t\n\t\t<figure class=\"wpb_wrapper vc_figure\">\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"278\" src=\"https:\/\/stei.itb.ac.id\/wp-content\/uploads\/6.-Riset-GB-Prof-1.jpg\" class=\"vc_single_image-img attachment-full\" alt=\"\" title=\"6. Riset GB - Prof\" \/><\/div><figcaption class=\"vc_figure-caption\">Figure 2 Obtained 132 Hadamard Matrix<\/figcaption>\n\t\t<\/figure>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div><div class=\"fullwidth\" ><div class=\"vc_row wpb_row vc_row-fluid vc_custom_1734194817030\"><div class=\"wpb_column vc_column_container vc_col-sm-12\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h5><strong>Conclusion<\/strong><\/h5>\n<p>This study demonstrates the capability of QAOA to efficiently construct Hadamard matrices using universal quantum computers. By avoiding ancillary qubits, the method overcomes scalability challenges associated with quantum annealers, enabling the construction of larger matrices.<\/p>\n<p>The experiments confirmed exponential performance improvements and validated the scalability of QAOA for higher-order matrix searches. These findings underscore the potential of gate-based quantum systems in addressing complex optimization problems.<\/p>\n<p>Future work will focus on noise reduction, extending QAOA to unexplored matrix orders, and testing the approach on physical quantum hardware. This progress is expected to further solidify the role of quantum computing in solving previously intractable problems.<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"Kembali ke Beranda Prof. Andriyan Bayu Suksmono, PhD. Sekolah Teknik Elektro dan Informatika Abstract Finding Hadamard matrices is a computationally intensive problem due to the exponential growth of possible binary [...]","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-23423","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/pages\/23423","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/comments?post=23423"}],"version-history":[{"count":6,"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/pages\/23423\/revisions"}],"predecessor-version":[{"id":23433,"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/pages\/23423\/revisions\/23433"}],"wp:attachment":[{"href":"https:\/\/stei.itb.ac.id\/en\/wp-json\/wp\/v2\/media?parent=23423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}