Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Advanced Computer Information Technologies (ACIT)

Solving 2 by 2 Grid Sudoku Problem using Grover’s Algorithm with Intel Quantum SDK

Tejas Shinde, Yaknan John Gambo, Kevin Rasch, Helena Liebelt, Rui Li

Published Sep 21, 2023• 2 citations
Publisher

Abstract

Quantum technologies are moving towards enabling real world uses and as these technologies develop. The most important thing that differs Quantum from classical computers is that Quantum Computers can do “multiple” tasks at the same time as opposed to the classical computers doing a single task at a time. This phenomenon has led to the discovery of a few algorithms that are faster than regular computers. One such algorithm is the Grover’s Algorithm[l]. This algorithm has shown a few real-world applications such as Quantum Search Algorithm, Travelling salesman, etc[2]. In this paper, Grover’s algorithm is introduced, and a 2 x 2 Sudoku example is solved using Intel Quantum Software Development Kit[3]. The Intel Quantum SDK is quite new and in this paper we show how a simple Grover’s Problem can be implemented in the SDK. Sudoku is a popular number-based puzzle game played on a grid consisting of nine squares subdivided into smaller 3x3 grids. The objective is to fill the grid with numbers from 1 to 9, ensuring that each row, column, and 3x3 grid contains all numbers exactly once.

DOI
10.1109/acit58437.2023.10275442

Related papers

Sudoku Solving Using Quantum Computer

Varun Singh, Varun Sharma, Vasu Bachchas , Deepanshu kaushik

We use ability of quantum computing such as superposition and entanglement to solve the sudoku. In recent years, quantum computers have shown promise as a new technology for solving complex problems in various fields, including optimization and cryptography. In this paper, we investigate the potential of quantum computers for solving Sudoku puzzles. We present a quantum algorithm for solving Sudoku puzzles, and compare its performance to classical algorithms. Our results show that the quantum algorithm outperforms classical algorithms in terms of both speed and accuracy, and provides a new tool for solving Sudoku puzzles efficiently. Additionally, we discuss the implications of our results for the development of quantum algorithms for solving other combinatorial problems.

Journal of Pharmaceutical Negative Results•Dec 31, 2022•2 citations

Sudoku Solving Using Quantum Computer

Varun Singh, Varun Sharma, Vasu Bachchas

Abstract: We use ability of quantum computing such as superposition and entanglement to solve the sudoku. In recent years, quantum computers have shown promise as a new technology for solving complex problems in various fields, including optimization and cryptography. In this paper, we investigate the potential of quantum computers for solving Sudoku puzzles. We present a quantum algorithm for solving Sudoku puzzles, and compare its performance to classical algorithms. Our results show that the quantum algorithm outperforms classical algorithms in terms of both speed and accuracy, and provides a new tool for solving Sudoku puzzles efficiently. Additionally, we discuss the implications of our results for the development of quantum algorithms for solving other combinatorial problems.

International Journal for Research in Applied Science and Engineering Technology•Feb 16, 2023•2 citations

Solving Sudoku game using a hybrid classical-quantum algorithm

Ankur Kumar Pal, Sanghita Chandra, Vardaan Mongia +2 more

Sudoku is a fun combinatorial game, based on the Latin square, which has wide applications as being an efficient design in controlling multiple sources of variable nuisance simultaneously. Quantum Sudoku solver uses basics of quantum mechanics such as superposition and entanglement. Using the concept of duality quantum computing, we propose an algorithm which solves a 4 × 4 Sudoku puzzle with a space complexity [ O ( N 2 ( 4 + log ⁡ ( N ) ) ] (where N = 4). Our proposed algorithm has a primary aim to provide a theoretical framework for an application of duality quantum computing.

Europhysics Letters (EPL)•Jan 31, 2020•15 citations

A Resource Efficient Ising Model‐Based Quantum Sudoku Solver

Wen-Li Wang, Mei-Huei Tang, Kevin Wang +3 more

ABSTRACT Background Quantum algorithms exploit superposition and parallelism to address complex combinatorial problems, many of which fall into the non‐polynomial (NP) class. Sudoku, a widely known logic‐based puzzle, is proven to be NP‐complete and thus presents a suitable testbed for exploring quantum optimization approaches. The Ising model—originally introduced for NP‐hard Ising spin glass problems—provides a natural mathematical framework for expressing constraints in a form amenable to quantum computation. Objective This work aims to develop a quantum Sudoku solver inspired by the Ising model that minimizes the number of logical qubits required, making it suitable for today's resource‐limited quantum hardware. The broader goal is to demonstrate a modeling strategy that may generalize to other NP optimization problems. Methods The solver construction begins by translating Sudoku constraints into mathematical expressions represented through couplings of atomic spins. These constraints are formulated into observable operators using Pauli operators, enabling the calculation of expectation values over candidate quantum states. Individual quantum algorithmic components are then integrated into a global optimization pipeline. The performance and correctness of this solver are evaluated through the Quantum Approximate Optimization Algorithm (QAOA) combined with the COBYLA classical optimizer within the IBM Qiskit SDK. A code example illustrates the implementation of multiple puzzle constraints and the verification of the resulting quantum circuits. Results The modeling approach successfully encodes Sudoku rules into an Ising Hamiltonian with reduced qubit requirements. Preliminary evaluations using QAOA and COBYLA demonstrate that the solver can identify puzzle‐consistent solutions while maintaining low resource consumption. The quantum circuit construction matches theoretical expectations, and the code snippet confirms successful constraint enforcement within the Qiskit environment. Conclusions The proposed quantum Sudoku solver highlights the potential of Ising‐based formulations to address NP optimization problems on near‐term quantum devices. By reducing logical qubit usage without sacrificing algorithmic integrity, this strategy may support broader applications in constrained optimization. The implementation serves as both a proof of concept and a practical guide for extending Ising‐inspired quantum modeling to other NP‐hard domains.

Software Practice and Experience•Mar 15, 2026•1 citation

Implementation of Grover's Algorithm based on Quantum Reservoir Computing

Shivani Mehta, Vidya Praveen Bhallamudi, Arige Sumanth +1 more

Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.

International Conference for Emerging Technology (INCET)•May 24, 2024•2 citations

Implementation of Efficient Quantum Computing Algorithm for Searching

Nirhali Atharva, Malwade Rohit, P. Akshay +2 more

The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.

International Research Journal on Advanced Engineering Hub (IRJAEH)•May 21, 2025•0 citations
Quantum technologies are moving towards enabling real world uses and as these technologies develop. The most important thing that differs Quantum from classical computers is that Quantum Computers can do “multiple” tasks at the same time as opposed to the classical computers doing a single task at a time. This phenomenon has led to the discovery of a few algorithms that are faster than regular computers. One such algorithm is the Grover’s Algorithm[l]. This algorithm has shown a few real-world applications such as Quantum Search Algorithm, Travelling salesman, etc[2]. In this paper, Grover’s algorithm is introduced, and a 2 x 2 Sudoku example is solved using Intel Quantum Software Development Kit[3]. The Intel Quantum SDK is quite new and in this paper we show how a simple Grover’s Problem can be implemented in the SDK. Sudoku is a popular number-based puzzle game played on a grid consisting of nine squares subdivided into smaller 3x3 grids. The objective is to fill the grid with numbers from 1 to 9, ensuring that each row, column, and 3x3 grid contains all numbers exactly once.
We use ability of quantum computing such as superposition and entanglement to solve the sudoku. In recent years, quantum computers have shown promise as a new technology for solving complex problems in various fields, including optimization and cryptography. In this paper, we investigate the potential of quantum computers for solving Sudoku puzzles. We present a quantum algorithm for solving Sudoku puzzles, and compare its performance to classical algorithms. Our results show that the quantum algorithm outperforms classical algorithms in terms of both speed and accuracy, and provides a new tool for solving Sudoku puzzles efficiently. Additionally, we discuss the implications of our results for the development of quantum algorithms for solving other combinatorial problems.
Abstract: We use ability of quantum computing such as superposition and entanglement to solve the sudoku. In recent years, quantum computers have shown promise as a new technology for solving complex problems in various fields, including optimization and cryptography. In this paper, we investigate the potential of quantum computers for solving Sudoku puzzles. We present a quantum algorithm for solving Sudoku puzzles, and compare its performance to classical algorithms. Our results show that the quantum algorithm outperforms classical algorithms in terms of both speed and accuracy, and provides a new tool for solving Sudoku puzzles efficiently. Additionally, we discuss the implications of our results for the development of quantum algorithms for solving other combinatorial problems.
Sudoku is a fun combinatorial game, based on the Latin square, which has wide applications as being an efficient design in controlling multiple sources of variable nuisance simultaneously. Quantum Sudoku solver uses basics of quantum mechanics such as superposition and entanglement. Using the concept of duality quantum computing, we propose an algorithm which solves a 4 × 4 Sudoku puzzle with a space complexity [ O ( N 2 ( 4 + log ⁡ ( N ) ) ] (where N = 4). Our proposed algorithm has a primary aim to provide a theoretical framework for an application of duality quantum computing.
ABSTRACT Background Quantum algorithms exploit superposition and parallelism to address complex combinatorial problems, many of which fall into the non‐polynomial (NP) class. Sudoku, a widely known logic‐based puzzle, is proven to be NP‐complete and thus presents a suitable testbed for exploring quantum optimization approaches. The Ising model—originally introduced for NP‐hard Ising spin glass problems—provides a natural mathematical framework for expressing constraints in a form amenable to quantum computation. Objective This work aims to develop a quantum Sudoku solver inspired by the Ising model that minimizes the number of logical qubits required, making it suitable for today's resource‐limited quantum hardware. The broader goal is to demonstrate a modeling strategy that may generalize to other NP optimization problems. Methods The solver construction begins by translating Sudoku constraints into mathematical expressions represented through couplings of atomic spins. These constraints are formulated into observable operators using Pauli operators, enabling the calculation of expectation values over candidate quantum states. Individual quantum algorithmic components are then integrated into a global optimization pipeline. The performance and correctness of this solver are evaluated through the Quantum Approximate Optimization Algorithm (QAOA) combined with the COBYLA classical optimizer within the IBM Qiskit SDK. A code example illustrates the implementation of multiple puzzle constraints and the verification of the resulting quantum circuits. Results The modeling approach successfully encodes Sudoku rules into an Ising Hamiltonian with reduced qubit requirements. Preliminary evaluations using QAOA and COBYLA demonstrate that the solver can identify puzzle‐consistent solutions while maintaining low resource consumption. The quantum circuit construction matches theoretical expectations, and the code snippet confirms successful constraint enforcement within the Qiskit environment. Conclusions The proposed quantum Sudoku solver highlights the potential of Ising‐based formulations to address NP optimization problems on near‐term quantum devices. By reducing logical qubit usage without sacrificing algorithmic integrity, this strategy may support broader applications in constrained optimization. The implementation serves as both a proof of concept and a practical guide for extending Ising‐inspired quantum modeling to other NP‐hard domains.
Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.
The K-SAT problem is a fundamental challenge in computational theory, widely used in artificial intelligence, cryptography, and optimization. Classical algorithms struggle with exponential time complexity, making them inefficient for large-scale instances. In this research, we propose an efficient quantum computing approach based on Grover’s algorithm to enhance the search process for satisfiable solutions in K-SAT problems. Our implementation leverages quantum superposition and amplitude amplification to explore multiple possible solutions simultaneously, reducing the search complexity from O (2ⁿ) in classical methods to O(√2ⁿ) in quantum computing. We design a quantum oracle that encodes the K-SAT clauses and integrates it into Grover’s iterative search framework. The performance is evaluated through Qiskit simulations, demonstrating a significant improvement in search efficiency compared to classical brute-force techniques. The results highlight the potential of quantum algorithms in solving complex combinatorial problems with enhanced speed and accuracy. This study contributes to the development of quantum-accelerated optimization methods, paving the way for real-world applications in machine learning, cryptanalysis, and large-scale data processing.