@article{MTMT:37417328,
	title = {Resident Fitness Computation in Linear Time and Other Algorithmic Aspects of Interacting Trajectories},
	url = {https://m2.mtmt.hu/api/publication/37417328},
	author = {Friedl, Katalin and Nemkin, Viktória and Tóbiás, András József},
	doi = {10.1002/rsa.70087},
	journal-iso = {RANDOM STRUCT ALGOR},
	journal = {RANDOM STRUCTURES & ALGORITHMS},
	volume = {69},
	unique-id = {37417328},
	issn = {1042-9832},
	abstract = {Systems of interacting trajectories were recently studied in Hermann et al. (2025). Such a system of ‐valued piecewise linear trajectories arises as a scaling limit of the system of logarithmic subpopulation sizes in a population‐genetic model (more precisely, a Moran model) with mutation and selection. By definition, the resident fitness is initially 0 and afterward it increases by the ultimate slope of each trajectory that reaches height 1. We show that although the interaction of trajectories may yield slope changes in total, the resident fitness function can be computed algorithmically in time. Our algorithm uses the so‐called continued lines representation of the system of interacting trajectories. In the special case of Poissonian interacting trajectories (PIT), where the birth times of the trajectories form a Poisson process, and the initial slopes are random and i.i.d., we provide a linear bound on the expected total number of slope changes.},
	year = {2026},
	eissn = {1098-2418},
	pages = {1-20}
}

@article{MTMT:36181166,
	title = {San Vitale Challenge: Automatic Reconstruction of Ancient Colored Glass Windows},
	url = {https://m2.mtmt.hu/api/publication/36181166},
	author = {Di Domenico, Nicolò and Borghi, Guido and Franco, Annalisa and Boschetti, Marco and Giacomini, Federica and Barzaghi, Sebastian and Ferucci, Silvia and Zambruno, Simone and Mularoni, Lorenzo and Gao, Qiong and Che, Chenyue and Li, Guoxin and Zu, Yanyan and Hao, Jiayao and Zhang, Junpei and Dúcz, Ákos and Gegő, Levente and Imeri, Klevis and Nemkin, Viktória and Rakhmatillaev, Azam and Szatmári, Soma and Rowan, William},
	doi = {10.1007/978-3-031-91572-7_16},
	journal-iso = {LNCS},
	journal = {LECTURE NOTES IN COMPUTER SCIENCE},
	volume = {LNCS},
	unique-id = {36181166},
	issn = {0302-9743},
	abstract = {The sixth-century Basilica of San Vitale in Ravenna, Italy, once featured intricate circular colored glass windows that illuminated its interior. Although these windows are now lost, several fragments were recovered during recent restorations. Unfortunately, reconstructing the original glass windows from these fragments is extremely complex and time-consuming, requiring the use of specialized expertise. Therefore, the development of automatic reconstruction techniques based on Artificial Intelligence is particularly important and challenging, due to, for instance, the presence of uniform color, damaged glass edges, and many fragment outliers. In this direction, the San Vitale Challenge was organized to gather the best methods and algorithms, as described and summarized in this paper. The challenge, split into several sub-tracks of increasing difficulty and realism, received the submission of several solutions, ranging from more classical computer vision algorithms to purely deep learning-based approaches, whose results are quantitatively evaluated and compared. In the last part of the paper, directions for future developments of such systems are discussed. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.},
	keywords = {expert systems; cultural heritage; Computer vision; Cultural heritages; Automatic reconstruction; Deep learning; Learning-based approach; Reconstruction techniques; Computer vision algorithms; glass windows; Automated puzzle solving; Glass fragments; Automated puzzle solving; Glass edges; Glass fragments},
	year = {2025},
	eissn = {1611-3349},
	pages = {263-278}
}

@CONFERENCE{MTMT:36283509,
	title = {A linear-time algorithm computing the resident fitness in interacting trajectories},
	url = {https://m2.mtmt.hu/api/publication/36283509},
	author = {Friedl, Katalin and Nemkin, Viktória and Tóbiás, András József},
	booktitle = {Proceedings of the 13th Hungarian–Japanese Symposium on Discrete Mathematics and Its Applications},
	unique-id = {36283509},
	year = {2025},
	pages = {469-479}
}

@CONFERENCE{MTMT:36187365,
	title = {Experiments with QUBO on D-Wave},
	url = {https://m2.mtmt.hu/api/publication/36187365},
	author = {Nemkin, Viktória and Alghazali, Qusay and Cinkler, Tibor and Friedl, Katalin and Kabódi, László},
	booktitle = {Proceedings of the 13th Hungarian–Japanese Symposium on Discrete Mathematics and Its Applications},
	unique-id = {36187365},
	year = {2025},
	pages = {289-296}
}

@inproceedings{MTMT:33716759,
	title = {Simulations of quantum walks on regular graphs},
	url = {https://m2.mtmt.hu/api/publication/33716759},
	author = {Friedl, Katalin and Nemkin, Viktória},
	booktitle = {Proceedings of the 12th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications},
	unique-id = {33716759},
	abstract = {We have developed a simulator program in Python that can execute classical and quantum random walks on regular graphs. The user implements the oracle (a function that returns the adjacency list for a given vertex) and the quantum coin used in the simulation. The software simulates the walk and produces a Latex report file detailing the results. Running several simulations, we compared the behavior of classical and coined quantum walks on some regular graphs and demonstrated the periodicity in a few small special cases. We present such reports with some mathematical explanations.},
	keywords = {simulation; Regular graphs; Quantum walks},
	year = {2023},
	pages = {373-381}
}

@misc{MTMT:34014788,
	title = {Application of Quantum Computing in Bioinformatics},
	url = {https://m2.mtmt.hu/api/publication/34014788},
	author = {Nemkin, Viktória},
	unique-id = {34014788},
	abstract = {Bioinformatics is an interdisciplinary field between computer science and biology. Its main goal is to answer biological questions by transforming them into computational problems and providing efficient algorithmic solutions. Researching bioinformatics significantly impacts our everyday lives, as discoveries in this field could help us solve many of today's major global problems. Utilizing them, we could create novel medical treatments, advance our understanding of genetic diseases, develop resistant crops to tackle a global food crisis or invent new technologies to decrease environmental pollution.
		
		Unfortunately, many practical problems in bioinformatics turn out to be computationally hard ones on classical hardware. Despite tremendous research effort to date, no sufficiently fast, deterministic solutions have been found to these problems.
		
		Quantum informatics is a compelling field for algorithmic research since quantum computers work fundamentally differently from classical ones, which means that the already established classical problem complexities are different in the quantum world. One of the most famous examples is Shor's prime factorization algorithm, which could break modern-day encryption quickly on a large-scale quantum computer.
		
		Due to this, governmental entities and global corporations are paying increased attention to quantum computing, and they are investing in quantum hardware and software development. For example, the European Commission started Quantum Flagship in 2018, a large-scale 10-year initiative with €1 billion in funding for quantum research, currently running under the Horizon Europe initiative.
		
		While quantum computing is still in its early stages and the limits of quantum hardware are yet unknown, the availability of a different computational model has already made new theoretical discoveries possible in both the classical and the quantum worlds.
		
		In my dissertation, I present a general overview of some computational problems in bioinformatics, particularly protein folding, and explain its connection to Grover's search algorithm and quantum walks. Then, I introduce the toolkit of quantum computation, specifically quantum walks and Grover's search algorithm. I present the mathematical framework for quantum walks, formulated in a way which is less common in literature, from which implementation follows naturally, and demonstrate their characteristics using the visualization software I have written. I describe the current practical problems with experimenting on quantum algorithms, specifically quantum protein folding, then design and implement a framework which can reduce some of these issues.},
	year = {2023}
}

@misc{MTMT:34014781,
	title = {Optimizing memory usage in quantum algorithm simulation},
	url = {https://m2.mtmt.hu/api/publication/34014781},
	author = {Nemkin, Viktória},
	unique-id = {34014781},
	abstract = {The quantum algorithm execution frameworks currently available on the market (IBM
		Qiskit, Google Cirq) implement their computations using unitary matrices of exponential
		size in the number of qubits. Consequently, they require large amounts of memory, even
		for small inputs. Although existing frameworks use some optimization methods, these
		often cannot provide improvements of an order of magnitude (e.g. sparse matrix storage
		mode) or are only applicable in special cases (Clifford gates). In practice, in contrast to
		a large company, the average user cannot experiment within reasonable limits, for many
		algorithms, even with relatively small inputs, as this would incur outstanding hardware
		costs.
		
		Algorithms that save memory in exchange for increased runtime can reduce these hardware
		expenses. For example, any submatrix of the unitary matrix can be computed on-the-fly
		during runtime, or the equivalent conventional algorithm can replace the unitary matrix
		operation. Although the currently available frameworks are open-source, they store the
		unitary matrices in memory as an integral part of their architecture, making it impossible
		to incorporate these memory optimization techniques.
		
		In my paper, I focus on developing these memory optimization methodologies and implementing them in a general-purpose quantum algorithm simulation framework. I present
		the classical algorithm and architecture design steps that form the basis of the system and
		demonstrate how this system can be used in quantum algorithm research. The framework
		is primarily intended to be used in a resource-constrained environment to enable running
		tests on a larger number of qubits, thus facilitating theoretical research. Accordingly, I will
		make the system and its documentation available to everyone in an open-source licensed
		form.},
	year = {2022}
}

@misc{MTMT:34014812,
	title = {Simulation of quantum walks on a classical computer},
	url = {https://m2.mtmt.hu/api/publication/34014812},
	author = {Nemkin, Viktória},
	unique-id = {34014812},
	abstract = {In recent years, there has been an increasing focus on quantum informatics. Influential global companies such as IBM, Google, Microsoft, and Amazon have invested significant amounts into studying and developing hardware and software for this sector, while the European Union and Hungary have launched several programs to accelerate quantum research.
		
		Current technology is yet to produce a significant number of qubits (quantum bits) in a quantum processor, but many believe the amount will increase over the years. The first practical quantum algorithms to be run on these processors are likely to be the ones that use qubits sparingly. Quantum walking, the generalized version of classical random walking, is exactly this kind of algorithm. The number of qubits required to run a quantum walk on a graph is logarithmic in the number of vertices, making it a promising technique for the near future. Furthermore, Grover's search algorithm (a basis for many quantum algorithms) can be viewed as a special case of quantum walks, which illustrates the potential power of this method.
		
		In my dissertation, I present the mathematical framework for quantum walks, detailing the points critical for implementation, which are given less emphasis in the literature. I describe the architecture and capabilities of the simulator program I have written and the conclusions of the simulations I have run.
		
		I developed the software using Python 3, based on the Strategy design pattern. It supports graphs commonly found in the literature while also providing a method for combining them, facilitating experimentation on several kinds of regular graphs. This composition is also the foundation of the quantum walk. It can simulate classical and quantum walks on the same graphs and produce a report file detailing the results. In the quantum case, the characteristics of the walk are also dependent on the type of coin used to generate the probabilities, which can be defined in several ways. The program includes the Hadamard, Grover, and Fourier coins and can easily be extended with others.
		
		Running several simulations, I compared the behavior of classical and quantum walks and demonstrated the quantum characteristics expected from the theoretical literature, the ballistic nature of the Hadamard walk, and the cyclic property of quantum walks.},
	year = {2021}
}