SudoQ -- a quantum variant of the popular game

We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical (commutative) setting. We introduce and analyze a randomized algorithm for computing solutions of SudoQ puzzles. Finally, we state two important conjectures relating the quantum and the classical solutions of SudoQ puzzles, corroborated by analytical and numerical evidence.Comment: Python code and examples available at https://github.com/inechita/Sudo

EVOLUTIONARY MATHEMATICS AND SCIENCE FOR SUDOKU9.0: EASY WAY TO CRACK HARD SUDOKU WITH THE PRINCIPLE OF THE LEAST CHOICE

Tsao, Hung-ping 曹恆平 (2021). Evolutionary mathematics and arts Sudoku9.0: Easy Way to Crack Hard Sudoku with the Principle of the Least Choice. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. 王抗曝 and Tsao, Hung-ping 曹恆平 (editors). Volume 3, Number 10, October 2021; 42 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL3-NUM10-OCT2021; ISBN 978-0-9890870-3-2. ............ABSTRACT: The single most common feature of hard Sudoku puzzles is to defy the solver’s logical thinking. So to solve those puzzles, we need to use the counter logic. Accordingly, we introduce here the Principle of the Least Choice (PLC) to settle the multiple choice situations. With this novel strategy, we demonstrate how easy it is to crack down five well-known hardest puzzles ever designed. ..........KEYWORDS: Sudoku, Puzzle, Row move, Column move, Block move, Box move, Grid move, Terminating move, Law of unique solution, Candidate, Principle of the Least Choice. Therefore we solemnly declare that SUDOKU9.0 turns “Sudoku of level 9” into a “Piece of cake”

Automatic Solutions of Logic Puzzles

Thesis advisor: Howard StraubingThe use of computer programs to automatically solve logic puzzles is examined in this work. A typical example of this type of logic puzzle is one in which there are five people, with five different occupations and five different color houses. The task is to use various clues to determine which occupation and which color belongs to each person. The clues to this type of puzzle often are statements such as, ''John is not the barber,'' or ''Joe lives in the blue house.'' These puzzles range widely in complexity with varying numbers of objects to identify and varying numbers of characteristics that need to be identified for each object. With respect to the theoretical aspects of solving these puzzles automatically, this work proves that the problem of determining, given a logic puzzle, whether or not that logic puzzle has a solution is NP-Complete. This implies, provided that P is not equal to NP, that, for large inputs, automated solvers for these puzzles will not be efficient in all cases. Having proved this, this work proceeds to seek methods that will work for solving these puzzles efficiently in most cases. To that end, each logic puzzle can be encoded as an instance of boolean satisfiability. Two possible encodings are proposed that both translate logic puzzles into boolean formulas in Conjunctive Normal Form. Using a selection of test puzzles, a group of boolean satisfiability solvers is used to solve these puzzles in both encodings. In most cases, these simple solvers are successful in producing solutions efficiently.Thesis (BS) — Boston College, 2009.Submitted to: Boston College. College of Arts and Sciences.Discipline: College Honors Program.Discipline: Computer Science

An overview of sparse convex optimization

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. Optimization is seeking values of a variable that leads to an optimal value of the function that is to be optimized. Suppose we have a system of equations where there more unknowns than the equations. This type of system leads to an infinitely many solution. If one has prior knowledge that the solution is sparse this problem can be treated as an optimization problem. In this mini-dissertation we will discuss the convex algorithms for finding sparse solution. We use convex algorithm are chosen since they are relatively easy to implement. The class of methods we will discuss are convex relaxation, greedy algorithms and iterative thresholding. We will then compare this algorithms by applying them to a Sudoku problem.Dissertation (MSc)--University of Pretoria, 2018.CAIR and STATOMETStatisticsMScUnrestricte

Quantum Search Algorithms for Constraint Satisfaction and Optimization Problems Using Grover\u27s Search and Quantum Walk Algorithms with Advanced Oracle Design

The field of quantum computing has emerged as a powerful tool for solving and optimizing combinatorial optimization problems. To solve many real-world problems with many variables and possible solutions for constraint satisfaction and optimization problems, the required number of qubits of scalable hardware for quantum computing is the bottleneck in the current generation of quantum computers. In this dissertation, we will demonstrate advanced, scalable building blocks for the quantum search algorithms that have been implemented in Grover\u27s search algorithm and the quantum walk algorithm. The scalable building blocks are used to reduce the required number of qubits in the design. The proposed architecture effectively scales and optimizes the number of qubits needed to solve large problems with a limited number of qubits. Thus, scaling and optimizing the number of qubits that can be accommodated in quantum algorithm design directly reflect on performance. Also, accuracy is a key performance metric related to how accurately one can measure quantum states. The search space of quantum search algorithms is traditionally created by using the Hadamard operator to create superposition. However, creating superpositions for problems that do not need all superposition states decreases the accuracy of the measured states. We present an efficient quantum circuit design that the user has control over to create the subspace superposition states for the search space as needed. Using only the subspace states as superposition states of the search space will increase the rate of correct solutions. In this dissertation, we will present the implementation of practical problems for Grover\u27s search algorithm and quantum walk algorithm in logic design, logic puzzles, and machine learning problems such as SAT, MAX-SAT, XOR-SAT, and like SAT problems in EDA, and mining frequent patterns for association rule mining