NWAOKOCHA, M. Shorův algoritmus v kvantové kryptografii [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2021.

Posudek vedoucího

Hrdina, Jaroslav

The thesis deals with one of the basic algorithms of quantum cryptography, Shor's algorithm. After the introduction, Chapter two explains the basics of the mathematical apparatus which is needed for quantum computing generally. In Chapter three the author introduces Shor's algorithm and discuss its complexity. Finally, in chapter four the author presents hos implementation in the IBM Quiskit environment. The core of the work is quantum Fourier transform which is explained correctly and in details. I especially appreciate the fact that the author worked individually on theoretical background and also on implementation. I recommend the thesis to be defended.

Posudek oponenta

Vašík, Petr

Typography and English • page. 5, math font for function „log“, math fonts for symbols in text e.g. page 10 – U and B, the same for the gates, X,Z etc. The fonts are used rather randomly throughout the whole text. • commas and full stops in assertions • there is no numbering of assertions and no cross referencing until page 24 • page 15, par. C, z-axis – not Z-axis • sometimes unclear if you are talking about n qubits or n-qubits, like on page 18 or 26 • sect. 2.1.7, undefined and unclear terms of target and control • sect. 2.2.1 computational complexity instead of hardness • factorisation vs. factoring (page 22) • when listing various types of encrypting algorithms, sect 2.2.1 and 2.2.2, references would be appropriate. Otherwise it is just a list of names with no information included. • Page 25 – the text is far out of the page margins • Page 25 – sometimes you use exp and sometimes e^ • Fig. 3.2 overflew the page margin • When referring to equations, use \eqref (2) instead of \ref 2, e.g. page 29 • What does it mean that an equation peaks near some value? Notation • page 9 – three types of notation for reals, complex numbers and vectors (\alpha, \gamma, a, x) • one terminology should be dominant, this holds also for notions of qubit, state, statevector, measurement and gate (mixed on pages 15 and 16) • sect. 2.1.6 undefined notion of complex amplitude • It is necessary to distinguish between established symbols (e for Euler’s number) and the same symbols (e) introduced in the text (page 22) • Page 26, assertion (3.2) is almost 1:1 copy from Qiskit, furthermore it overflew the page margin • Page 28, the notion of a phase kickback is undefined Math • definition of tensor product – why for dimension 2? • later, in sect. 2.1.6 you start using \times in the formula for tensor product • page 11, last line – not true for general \alpha real and \tilde{\alpha} complex. What is the relation between \ alpha and \tilde{\alpha}? • State |+> mentioned for the first time but defined later • Fig. 2.4 – explain, the result is a composition of the two states in the figure? • Fig. 2.7 is very poorly commented and thus confusing • First assertion of sect 2.2.2 is completely without description of variables included and thus incomprehensible • If introducing a notion (QFT, DFT, wavefunction – sect. 3.1) without any specification, it is necessary to provide a reference! Moreover, the notions must be specified, e.g. in DFT definition, vector x is real or complex? Vector y is then complex. The text is sometimes too brief (especially the lists of known encryption methods) to suit the form of a thesis. This may be caused by the number of methods and notions that the author included in the text which, in the end, moved the text rather towards a survey than to a thesis. Especially when introducing encrypting algorithms, some more continuous text with more precise mathematical explanation would be appropriate. As an example of inaccurate formulation we refer to a sentence “As the QFT circuit becomes larger, an increasing amount of time is spent doing increasingly slight rotations.“ on page 26. Indeed, the text is mostly taken from Qiskit manual, including formulae, calculations, figures etc., with minor changes in the text. Because Qiskit is rather a free composition of chapters, the reason for discontinuity is obvious. Some parts are missing precise object specification which leads to confusions. Copied figures often overflow the page margins (see e.g. Fig. 3.1, 4.1, 4.2, page 49 etc.). Overall, the student interpreted a manual to Qiskit software, yet with many mathematical inaccuracies, graphical issues and in a not very fluent way with many explanations missing, and then he calculated an example in Qiskit tutorial on Shor’s algorithm. In my opinion, this is enough for the diploma thesis only if the student proves that he understands all parts of the text, which indeed describes a very sophisticated problem. His understanding to the calculations, theorems and algorithms is not clear from the text itself. Therefore, I suggest degree E for the thesis and I recommend the committee to consider different evaluation only after student’s explanation.

eVSKP id 131939