Browsing by master's degree program "Teoreettisten ja laskennallisten menetelmien maisteriohjelma (Theoretical Calculation Methods)"
Now showing items 41-46 of 46
-
(2024)A quantum computer is a new kind of computer which utilizes quantum phenomena in computing. This machine has the potential to solve specific tasks faster than the most powerful supercomputers and therefore has potential real-life applications across various sectors of society. One promising approach to realize a quantum computer is to store information in superconducting qubits, which are artificial two-level quantum systems made from superconducting electrical circuits. Extremely precise control of these qubits is essential but also challenging due to the excitations out of the two lowest energy states of the quantum system that constitute the computational subspace. In this thesis, we propose a new way to control a superconducting multimode qubit using the unimon qubit as an example. By coupling differently to the different modes of the multimode qubit circuit, we cancel the transition from the first excited state to the second excited state, which is typically the main transition causing a leakage out of the computational subspace. We present a theoretical description of this model by utilizing methods of circuit quantum electrodynamics to compute the energy spectrum and the transition matrix elements of the qubit. By using these results, we simulate the dynamics of the driven unimon qubit undergoing as a single-qubit gate. The result of the simulation shows that this method decreases the leakage relative to the conventional method of driving a qubit, where only one external drive is applied. However, by improving the conventional method with a more advanced pulse optimization method, the leakage becomes smaller than in the standard case of two drive fields. In addition, we find that the practical implementation of our method may be sensitive to variations in the qubit parameters. Therefore, the practical implementation of the method needs further research in the future. By cancelling one energy-level transition of the qubit, we find that other transitions in modes of similar frequency were strongly suppressed. Therefore, this method might be potentially utilized in other qubit operations than the quantum gates, such as in the qubit resetting process, where driving to higher frequency modes of the unimon is preferred.
-
(2023)One of the main questions in nuclear astrophysics is whether deconfined quark matter exists inside neutron stars. In order to answer this, the equation of state (EoS) of cold and dense quark matter, which plays an essential role in finding the equation of state of strongly interacting matter (QCD matter) inside neutron stars, needs to be determined as accurately as possible [14, 25]. The equation of state, or the pressure, of cold and dense quark matter was evaluated to the full three-loop order in perturbation theory back in 1977 by Freedman and McLerran [9, 10] and recently the contributions of the soft momentum scale to the four-loop pressure were evaluated in [13, 14, 15]. What is missing from the full four-loop pressure is the contribution of the hard momentum scale μ. In this thesis we shall first evaluate the known result for one three-loop Feynman diagram contributing to the three-loop pressure. After this, we derive a new result for a fermionic four-loop master integral at zero temperature and finite quark chemical potentials, which directly contributes to the yet unknown hard sector of the four-loop pressure of cold and dense quark matter.
-
(2023)Fysikaalisten kenttien rakenteista solmittuja linkkejä ja solmuja on osoitettu esiintyvän useissa eri systeemeissä, optisista ja akustisista kentistä aina supranesteisiin. Tällaisten solmujen evoluutio ideaaleissa systeemeissä rajoittuu perinteisten solmujen, kuten kengännauhoista löytyvien, tyyppiseksi. Fysikaalisissa systeemeissä, joissa energiahäviöt ovat mahdollisia, mahdolliset evoluutiot ovat eksoottisempia; kentässä olevan solmun säikeet --- kentän topologisten pyörteiden ytimet --- voivat mahdollisesti kokea solmun topologiaa muuttavia evoluutioita ja purkautua erillisiksi solmuttomiksi silmukoiksi. Hyödyntämällä väritettyä linkkidiagrammiesitystä osoitamme yllä mainittuja evoluutioita välttävien topologisesti suojattujen pyörresolmujen olemassaolon spin-2 Bosen--Einsteinin kondensaatin syklisessä faasissa. Nämä ovat ensimmäiset suojatut pyörresolmut, jotka on löydetty fysikaalisesti toteutettavasta systeemistä. Todistuksessa käytetty väritysformalismi on yleinen viitekehys. Sitä voidaan soveltaa useisiin muihin systeemeihin, kunhan näiden järjestysparametriavaruuksien toinen homotopiaryhmä on triviaali. Syklisen faasin pyörresolmut ja -linkit mahdollistavat myös osittaisen luokittelun: jokainen solmu on ekvivalentti joukkoon irtonaisia apilasolmuja ja/tai kahdeksikkosolmuja, tai on triviaali. Kokonaislukuaskelin kvantittuneista pyörteistä muodostuvat linkit ovat ekvivalentteja joko Borromeon renkaisiin, suljettuun kolmen silmukan ketjuun tai triviaaliin silmukkaan.
-
(2022)The Traveling Salesman Problem (TSP) is a well-known optimization problem. The time needed to solve TSP classically grows exponentially with the size of the input, placing it into the NP-hard computational complexity class–the class of problems that are at least as hard as any other problem solvable in nondeterministic polynomial time. Quantum computing gives us a new approach to searching through such a huge search space, using methods such as quantum annealing and phase estimation. Although the current state of quantum computers does not give us enough resources to solve TSP with a large input, we can use quantum computing methods to improve on existing classical algorithms. The thesis reviews existing methods to efficiently tackle TSP utilizing potential quantum resources, and discusses the augmentation of classical algorithms with quantum techniques to reduce the time complexity of solving this computationally challenging problem.
-
(2024)Particle dark matter (DM) as a solution to the missing mass problem in astronomy has been examined widely and with different models. Among the most studied are weakly interacting massive particles, WIMPs, for short. As dark matter constitutes roughly a quarter of the energy budget of the universe, and due to its vital role in galaxy structures through gravitational interaction, the motivation to uncover the nature and properties of it is strong. In this master’s thesis, a specific particle dark matter model is examined. The model consists of a hidden dark sector added to the Standard Model of Particle Physics (SM). The dark sector introduces a new SU(2) gauge field that acts as a vector dark matter candidate, as well as a complex SU(2) scalar field and interactions between the two. Due to spontaneous symmetry breaking, the dark vector gains a non-zero mass. This relocation of degrees of freedom allows us to write the dark scalar field as having only one real degree of freedom. The dark scalar field also experiences mass mixing with the SM Higgs field, leaving the two propagating scalar mass eigenstates as superpositions of the dark scalar field and the Higgs field. One of these is then identified as the observed Higgs field with a mass of 125 GeV. The four free parameters of the model can be chosen as the masses of the dark matter candidate and the propagating dark scalar field, the angle of the rotation between mass and gauge eigenbasis in the scalar sector and the dark gauge coupling constant. To produce the observed relic density of dark matter, the DM particles need to pair-annihilate with a cross section of order 1.64 × 10^(−9) GeV^(−2). Further constraints are given by collider and direct detection experiments, leaving the parameter space of the model rather constrained. Depending on the values of the other free parameters, a viable mass range of around 100-200 GeV is found for the vector dark matter. The possibility of probing the properties of dark matter through experiments and observations exists. The existence and properties of the dark scalar field could be examined in the Large Hadron Collider. Possible phenomena in the scalar sector of the model, such as phase transitions, could be studied with upcoming gravitational wave detectors, namely the Laser Interferometer Space Antenna. Direct detection experiments provide a way of seeking the dark matter particle itself. With all these possibilities, the future seems interesting.
-
(2024)Cosmological first-order phase transitions (FOPTs) are a hypothetical scenario occurring in the early universe in which bubbles nucleate and expand, generating gravitational waves (GWs). These transitions interest scientists due to their occurrence in extensions to the Standard Model of particle physics, their potential for providing insight into open questions in particle physics and cosmology, and the possibility of observing their signature with the planned Laser Interferometer Space Antenna (LISA). Modeling GW production from FOPTs is thus a topic of active research. In FOPT models, GW production is split into three sources: collisions between bubble walls Ωenv, overlapping fluid shells Ωsw, and fluid turbulence Ωturb. When modeling the contribution from Ωsw in 1D spherical simulations, a sound shell model is often employed which assumes that fluid shells reach a calculable self-similar state of expansion before overlapping. In this thesis, I determine when this asymptotic expansion state is reached by defining and calculating a relaxation time ts and transition rate βs for 1D expanding fluid shells. I model two scenarios, a thin and a thick-walled perturbed nucleation bubble expanding in a relativistic fluid, in the limit of fast detonations and weak coupling. In each case, respectively, relaxation temperature and transition rate are determined to be: tsTc = 7.422(21) × 103, βs/Tc = 1.3474(38) × 10−4; and tsTc = 9.901(33) × 105, βs/Tc = 1.011(35) × 10−5. When fixing the critical temperature Tc below which bubbles can nucleate, these results predict that when the transition rate β > βs, the GW spectrum produced assuming relaxed fluid shells may be inaccurate. In addition to this main result, I also compare various methods for estimating bubble wall expansion velocity. These results are useful for 3D simulations, in which direct methods for determining wall velocity are unwieldy.
Now showing items 41-46 of 46