We expand the quantum variant of the popular game Sudoku by introducing the notion of cardinality of a quantum Sudoku (SudoQ), equal to the number of distinct vectors appearing in the pattern. Our considerations are focused on the genuinely quantum solutions---the solutions of size
N2 that have cardinality greater than
N2, and therefore cannot be reduced to classical counterparts by a unitary transformation. We find the complete parametrization of the genuinely quantum solutions of a $4\ifmmode\times\else\texttimes\fi{}4$ SudoQ game and establish that in this case the admissible cardinalities are 4, 6, 8, and 16. In particular, a solution with the maximal cardinality equal to 16 is presented. Furthermore, the parametrization enabled us to prove a recent conjecture of Nechita and Pillet [I. Nechita and J. Pillet, Quantum Inf. Comput. 21, 781 (2021)] for this special dimension. In general, we proved that for any
N it is possible to find an ${N}^{2}\ifmmode\times\else\texttimes\fi{}{N}^{2}$ SudoQ solution of cardinality
N4, which for a prime
N is related to a set of
N mutually unbiased bases of size
N2. Such a construction of
N4 different vectors of size
N yields a set of
N3 orthogonal measurements.
We expand the quantum variant of the popular game Sudoku by introducing the notion of cardinality of a quantum Sudoku (SudoQ), equal to the number of distinct vectors appearing in the pattern. Our considerations are focused on the genuinely quantum solutions, which are the solutions of size
N2 that have cardinality greater than
N2, and therefore cannot be reduced to classical counterparts by a unitary transformation. We find the complete parameterization of the genuinely quantum solutions of
4×4 SudoQ game and establish that in this case the admissible cardinalities are 4, 6, 8 and 16. In particular, a solution with the maximal cardinality equal to 16 is presented. Furthermore, the parametrization enabled us to prove a recent conjecture of Nechita and Pillet for this special dimension. In general, we proved that for any
N it is possible to find an
N2×N2 SudoQ solution of cardinality
N4, which for a prime
N is related to a set of
N mutually unbiased bases of size
N2. Such a construction of
N4 different vectors of size
N yields a set of
N3 orthogonal measurements.
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.
ABSTRACT Quantum Sudoku is the generalized version of the popular game Sudoku. A quantum Sudoku square is a special kind of quantum Latin square. A genuinely quantum solution of quantum Sudoku squares has been solved completely. In this paper, we introduce the notion of orthogonality of two quantum Sudoku squares. We establish three novel constructions of mutually orthogonal quantum Sudoku squares including Lorch construction, Pedersen‐Vis construction and direct product construction. As a result, we determine the genuinely quantum solution of a pair of orthogonal Sudoku squares of size for any positive integer . In general, we show that the resulting squares naturally define an absolutely maximally entangled state . Furthermore, we also show that the mutually orthogonal quantum Sudoku squares give rise to mutually unbiased bases based on maximally entangled states in for any prime power .
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.
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.