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      <abstractText>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.</abstractText>
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&lt;div class=&quot;lastModified&quot;&gt;Utolsó módosítás: 2026.01.26. 10:48 Háromszéki-Virág Fruzsina (MTMT Központi admin)
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	&lt;pre class=&quot;comment&quot; style=&quot;margin-top: 0; margin-bottom: 0;&quot;&gt;&lt;u&gt;Megjegyzés&lt;/u&gt;: WoS:hiba:001544981100016 2025-12-29 09:44 típus nem egyezik&lt;/pre&gt;

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Forrás	
	
	
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&lt;div class=&quot;funder&quot;&gt; 149835(Starting 149835) Támogató: Kulturális és Innovációs Minisztérium Nemzeti Kutatási Fejlesztési és Innovációs Alap,    MTA Bolyai Ösztöndíj(MTA Bolyai Ösztöndíj) Támogató: MTA Bolyai pályázat   &lt;/div&gt;
&lt;div class=&quot;lastModified&quot;&gt;Utolsó módosítás: 2025.09.03. 14:13 Szakonyi Erzsebet (RAMKI admin 4)
&lt;/div&gt;


        &lt;div class=&quot;lockedBy&quot;&gt;Központi kezelésű 2026.05.21. 14:36  Vasvari Lilian (MTMT Központ, admin)
        &lt;/div&gt;


	&lt;pre class=&quot;comment&quot; style=&quot;margin-top: 0; margin-bottom: 0;&quot;&gt;&lt;u&gt;Megjegyzés&lt;/u&gt;: This paper was supported by the Doctoral Excellence Fellowship Programme (DCEP), funded by the National Research, Development and Innovation Fund of the Ministry of Culture and Innovation and the Budapest University of Technology and Economics.
This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. Project no. STARTING 149835 has been implemented...&lt;/pre&gt;
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      <abstractText>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.</abstractText>
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      <title>Optimizing memory usage in quantum algorithm simulation</title>
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      <abstractText>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.</abstractText>
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      <title>Simulation of quantum walks on a classical computer</title>
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      <abstractText>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.</abstractText>
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