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.
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.
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.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
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, with its potential to revolutionize computation, relies fundamentally on the development of efficient algorithms to leverage its unparalleled processing capabilities. This research delves into the creation, exploration, and refinement of quantum computing algorithms, focusing on their applications in optimization, cryptography, and machine learning. Quantum algorithms such as Shor's and Grover's have demonstrated remarkable advantages in factorization and search problems, while more recent innovations are tackling complex challenges in global optimization and data analysis. By integrating principles of quantum mechanics—such as superposition, entanglement, and interference—these algorithms promise exponential speed-ups over classical counterparts in specific domains. This study critically analyzes existing quantum algorithms, proposes advancements in hybrid quantum-classical frameworks, and explores their implications for practical problem-solving. Through simulations and theoretical evaluations, it aims to bridge the gap between quantum theory and real-world applications, contributing to the evolution of quantum computing as a transformative technology.