SAJI, D. Řešení sudoku pomocí kvantového počítání [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2025.

Posudek vedoucího

Hrdina, Jaroslav

The original task of the thesis was completed relatively quickly, and the topic was gradually expanded with further perspectives on mathematical description. At the same time, unexpected problems arose during the implementation of higher-dimensional algebras (based on memory and hexadecimal representation of numbers). The topic thus developed in an interesting and unexpected direction. How is it possible to work in geometric algebra with a larger number of generators using appropriate mathematical apparatus.  For this purpose, the available computational resources were analyzed, and the most suitable method was selected. The student worked independently, and the thesis includes the theory, proposed solution, and implementation.

Posudek oponenta

Hildenbrand, Dietmar

This work is based on the example of the Quiskit tutorial [26] for a quantum computing solution of a 2x2 Sudoku. This is reasonable extended with an approach in order to compute important parameters such as the number of solutions. This 2x2 solution is then extended in a straightforward way to a 2x3 Sudoku. A drawback of the thesis is, that the state-of-the-art of other quantum computing based approaches is missing and not discussed. Since the simulation of the 2x3 Sudoku failed with Quiskit, an advantage of this work is, that also other promising mathematical tools to solve this problem are investigated and discussed. The structure of the thesis in principle is good, but, as already mentioned, the state of the art is missing. Also some important explanations are missing. The rules of Sudoku, for instance, are not explained. They can only be derived by the algorithm. The thesis also lacks of descriptions where it would be important to have some more detailed information as for instance in order to better understand Example 5.2.1. Also the listings and figures of the results of the quantum computing algorithms and how to interpret them could be explained in more detail. Some additional remarks: • Introduction: o „solve most of the problems“: better would be something like „solve many problems“ o Not completed sentence „support solving problems that classical computers ...“ o „From the 1980s, prominent results emerged in quantum mechanics“ seems to mean quantum computing • Figure 2.1: X is not explained • Section 5.4.9 „it takes inputs quantum bits“? • In the introduction of Chapt. 7 is the use of „Geometric Algebra“ and „Clifford Algebra“ confusing • Page 46: „from the from“ • In Chapt. 7.5 is the last sentence a bit confusing. It should be better used in Chapt. 7.6. • In the introduction of Chapt. 8, the last sentence seems to be not complete. • From the language point of view, there are some typos and the article „the“ is sometimes missing. • The reference [3] is wrong. GAALOP is not from Christian Perwass but from Christian Steinmetz and Dietmar Hildenbrand.

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