Browsing by master's degree program "Master's Programme in Theoretical and Computational Methods"
Now showing items 21-30 of 30
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(2023)Using quantum algorithms to carry out ML tasks is what is known as Quantum Machine Learning (QML) and the methods developed within this field have the potential to outperform their classical counterparts in solving certain learning problems. The development of the field is partly dependent on that of a functional quantum random access memory (QRAM), called for by some of the algorithms devised. Such a device would store data in a superposition and could then be queried when algorithms require it, similarly to its classical counterpart, allowing for efficient data access. Taking an axiomatic approach to QRAM, this thesis provides the main considerations, assumptions and results regarding QRAM and yields a QRAM handbook and comprehensive introduction to the literature pertaining to it.
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(2020)Hiukkasfysiikan standardimalli kuvaa alkeishiukkasia ja niiden välisiä vuorovaikutuksia. Higgsin bosonin löydön (2012) jälkeen kaikki standardimallin ennustamat hiukkaset on havaittu. Standardimalli on hyvin tarkka teoria, mutta kaikkia havaittuja asioita ei voida kuitenkaan selittää standardimallin puitteissa. Supersymmetria on yksi houkutteleva tapa laajentaa standardimallia. Matalan energian supersymmetriaa ei kuitenkaan ole havaittu. Supersymmetria vaatii toimiakseen niin sanotun kahden Higgsin dubletin mallin. Tavallisessa standardimallissa on yksi Higgsin dublettikenttä. Higgsin dubletissa on kaksi kompleksista kenttää eli yhteensä neljä vapausastetta, joten voisi olettaa, että siitä syntyy neljä hiukkasta. Kolme vapausasteista kuitenkin sitoutuu välibosoneihin W+, W− ja Z, jolloin jäljelle jää yksi Higgsin bosoni. Kahden Higgsin dubletin malleissa dublettikenttiä on kaksi. Koska se lisää teoriaan yhden neljän vapausasteen dubletin, Higgsin hiukkasia on siinä kaiken kaikkiaan viisi: kolme sähköisesti neutraalia (h, H ja A) sekä kaksi sähköisesti varattua (H+ ja H−). Tässä työssä keskitytään varattujen Higgsin hiukkasten etsintään malliriippumattomasti. Tutkimuksessa käytetään LHC-kiihdyttimen (Large Hadron Collider, suuri hadronitörmäytin) CMS-ilmaisimen (Compact Muon Solenoid, kompakti myonisolenoidi) keräämää dataa. Sähkövarauksellisten Higgsin bosonien etsintä keskittyy lopputiloihin, joissa varattu Higgsin bosoni hajoaa hadroniseksi tau-leptoniksi (eli tau-leptoniksi, joka puolestaan hajoaa hadroneiksi) sekä taun neutriinoksi. Niin sanottu liipaisu on tapa suodattaa dataa tallennusvaiheessa, sillä dataa tulee törmäyksistä niin paljon, ettei kaiken tallentaminen ole mahdollista. Eri liipaisimet hyväksyvät törmäystapauksia eri kriteerien perusteella. Liipaisusta aiheutuu merkittäviä systemaattisia epävarmuuksia. Tässä työssä liipaisun epävarmuuksia pyritään pienentämään käyttämällä sellaisia liipaisimia, joiden epävarmuudet ovat pienempiä. Tätä varten analyysi on jaettava riippumattomiin osiin, joiden epävarmuudet käsitellään erikseen. Lopuksi osat yhdistetään tilastollisesti toisiinsa, jolloin kokonaisepävarmuuden oletetaan pienenevän. Tässä työssä tutkitaan, pieneneekö tämä epävarmuus ja kuinka paljon. Näitä menetelmiä käyttäen kykenimme löytämään pieniä parannuksia analyysin tarkkuuteen raskaiden varattujen Higgsin bosonien kohdalla. Lisäksi odotettu raja, jota suurempi varatun Higgsin hiukkasen tuotto tässä lopputilassa olisi havaittavissa, paranee yllättävästi. Tätä rajan paranemista tutkitaan liipaisua emuloimalla. Työ on tarkoitus sisällyttää koko Run2:n datasta julkaistaviin tuloksiin.
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(2023)Particle jets are formed in high energy proton-proton collisions and then measured by particle physics experiments. These jets, initiated by the splitting and hadronization of color charged quarks and gluons, serve as important signatures of the strong force and provide a view to size scales smaller than the size of an atom. So, understanding jets, their behaviour and structure, is a path to understanding one of the four fundamental forces in the known universe. But, it is not only the strong force that is of interest. Studies of Standard Model physics and beyond Standard Model physics require a precise measurement of the energies of final state particles, represented often as jets, to understand our existing theories, to search for new physics hidden among our current experiments and to directly probe for the new physics. As experimentally reconstructed objects the measured jets require calibration. At the CMS experiment the jets are calibrated to the particle level jet energy scale and their resolution is determined to achieve the experimental goals of precision and understanding. During the many-step process of calibration, the position, energy and structure of the jets' are taken into account to provide the most accurate calibration possible. It is also of great importance, whether the jet is initiated by a gluon or a quark, as this affects the jets structure, distribution of energy among its constituents and the number of constituents. These differences cause disparities when calibrating the jets. Understanding of jets at the theory level is also important for simulation, which is utilized heavily during calibration and represents our current theoretical understanding of particle physics. This thesis presents a measurement of the relative response between light quark (up, down and strange) and gluon jets from the data of CMS experiment measured during 2018. The relative response is a measure of calibration between the objects and helps to show where the difference of quark and gluon jets is the largest. The discrimination between light quarks and gluons is performed with machine learning tools, and the relative response is compared at multiple stages of reconstruction to see how different effects affect the response. The dijet sample that is used in this study provides a full view of the phase space in pT and |eta|, with analysis covering both quark and gluon dominated regions of the space. These studies can then be continued with similar investigations of other samples, with the possibility of using the combined results as part of the calibration chain.
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(2020)First order electroweak phase transitions (EWPTs) are an attractive area of research. This is mainly due to two reasons. First, they contain aspects that could help to explain the observed baryon asymmetry. Secondly, strong first order PTs could produce gravitational waves (GWs) that could be detectable by the Laser Interferometer Space Antenna (LISA), a future space-based GW detector. However, the electroweak PT in the Standard Model (SM) is not a first order transition but a crossover. In so-called beyond the SM theories the first order transitions are possible. To investigate the possibility of an EWPT and the detection by LISA, we must be able to parametrise the nature of the PT accurately. We are interested in the calculation of the bubble nucleation rate because it can be used to estimate the properties of the possible GW signal, such as the duration of the PT. The nucleation rate essentially quantifies how likely it is for a point in space to tunnel from one phase to the other. The calculation can be done either using perturbation theory or simulations. Perturbative approaches however suffer from the so-called infrared problem and are not free of theoretical uncertainty. We need to perform a nonperturbative calculation so that we can determine the nucleation rate accurately and test the results of perturbation theory. In this thesis, we will explain the steps that go into a nonperturbative calculation of the bubble nucleation rate. We perform the calculation on the cubic anisotropy model, a theory with two scalar fields. This toy model is one of the simplest in which a radiatively induced transition occurs. We present preliminary results on the nucleation rate and compare it with the thin-wall approximation.
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(2024)Despite the continuous efforts to unveil the true nature of Dark Matter (DM), it still remains as a mystery. In this thesis we propose one model that can produce the correct relic abundance of DM in the current Universe, while fitting into the existing experimentally obtained constraints. In this model we add a singlet fermion, which is a not completely sterile right-handed neutrino, and a heavy real scalar singlet into the Standard Model of Particle Physics (SM) and carry out the relic density calculations. The DM candidate here is the singlet fermion, which acts as a thermally decoupled Weakly Interacting Massive Particle. Theoretical framework is laid out in detail. Special attention is given to obtaining the definition for relic abundance from Lee-Weinberg equation in terms of yield, and the decoupling temperature. It is found, that the usual way of handling the thermally averaged cross section appearing in these definitions is not suitable in this case. In fact, the usual approximations can only be done when thermally averaged cross section is almost linear in $s$, and this is a demand that very few models can satisfy. The correct way to treat the cross section by taking the expansion in terms of the relative velocity is presented with careful attention to detail. This methodology is then applied to the extension of the SM we introduced. Only tree-level processes are being considered. Cross sections are calculated for each possible process to obtain the total cross section needed for the DM relic density calculations. We present how the different free parameters in the theory affect the relic abundance and what masses are allowed for the right-handed neutrino to obtain. It is found out that the parameters in this model are heavily constrained. Yet the model is able to fit into the constraints obtained from branching ratio and direct detection (DD) experiments, while producing the correct relic density. This is true when the mixing angle $\theta$ is of the order $1 \times 10^{-4}$, and right-handed neutrino has the mass of exactly half of the mass of the heavy scalar or higher than the mass of the heavy scalar. It is proposed that allowing lepton mixing and adding a separate mass term for fermion in the model could make the model less restricted. Investigating this would be interesting thing to do in the future. However, the proposed DM candidate remains viable and the upcoming DD experiments will relatively soon reveal if the singlet fermion is the DM particle we are seeking.
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(2021)At the Compact Muon Solenoid (CMS) experiment at CERN (European Organization for Nuclear Research), the building blocks of the Universe are investigated by analysing the observed final-state particles resulting from high-energy proton-proton collisions. However, direct detection of final-state quarks and gluons is not possible due to a phenomenon known as colour confinement. Instead, event properties with a close correspondence with their distributions are studied. These event properties are known as jets. Jets are central to particle physics analysis and our understanding of them, and hence of our Universe, is dependent upon our ability to accurately measure their energy. Unfortunately, current detector technology is imprecise, necessitating downstream correction of measurement discrepancies. To achieve this, the CMS experiment employs a sequential multi-step jet calibration process. The process is performed several times per year, and more often during periods of data collection. Automating the jet calibration would increase the efficiency of the CMS experiment. By automating the code execution, the workflow could be performed independently of the analyst. This in turn, would speed up the analysis and reduce analyst workload. In addition, automation facilitates higher levels of reproducibility. In this thesis, a novel method for automating the derivation of jet energy corrections from simulation is presented. To achieve automation, the methodology utilises declarative programming. The analyst is simply required to express what should be executed, and no longer needs to determine how to execute it. To successfully automate the computation of jet energy corrections, it is necessary to capture detailed information concerning both the computational steps and the computational environment. The former is achieved with a computational workflow, and the latter using container technology. This allows a portable and scalable workflow to be achieved, which is easy to maintain and compare to previous runs. The results of this thesis strongly suggest that capturing complex experimental particle physics analyses with declarative workflow languages is both achievable and advantageous. The productivity of the analyst was improved, and reproducibility facilitated. However, the method is not without its challenges. Declarative programming requires the analyst to think differently about the problem at hand. As a result there are some sociological challenges to methodological uptake. However, once the extensive benefits are understood, we anticipate widespread adoption of this approach.
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(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.
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(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.
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(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.
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(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.
Now showing items 21-30 of 30