Advanced enough quantum computers promise to revolutionise fields such as cryptography, drug discovery and simulations of complex systems. Quantum computers are built on qubits which are fragile and susceptible to error-inducing interference, which is called noise. The aim of this study was to examine the effects of varying levels of noise interference on the success rate and runtimes of a quantum computer circuit design built to implement Shor’s quantum factorisation algorithm. This was conducted using the Qiskit framework for quantum computer simulation and custom noise model creation. Our results show a correlation between the level of noise interference on a circuit and the probability of getting the correct measurement. We also found a greater impact of readout errors on the success rates, one-qubit depolarising errors on runtimes and that two-qubit depolarising errors greatly affected both, which was also discussed in the study. Our findings are in line with previous research and help to highlight the importance of minimising errors on critical quantum logic gates in an algorithm. / Tillräckligt avancerade kvantdatorer lovar att revolutionera områden så som kryptografi, utveckling av nya läkemedel och simulering av komplexa system. Kvantdatorer är uppbyggda av qubits vilka är ömtåliga och mottagliga mot felinducerande interferens, vilket kallas brus. Målet med denna studie var att utforska effekten av varierande brusnivåers interferens på lyckade försök samt körtiden av en kvantdatorkrets designad för att implementera Shors algoritm. Detta gjordes med Qiskits ramverk för kvantdatorsimulering och anpassningsbara brusmodeller. Våra resultat visar en korrelation mellan nivån av brusinterferens på en krets och sannolikheten av att få den korrekt mätningen. Vi fann även en större påverkan av avläsningsfel på kvoten lyckade försök, en-qubit depolariserande fel på körtid och att två-qubit depolariserande fel hade en stor påverkan på båda, vilket vi även diskuterat i studien. Våra resultat är i linje med tidigare studier och hjälper till att lyfta fram vikten av att minimera inducerade fel på kritiska logiska grindar i en kvantdatoralgoritm.

In this thesis we study quantum-like representation and simulation of quantum algorithms by using classical computers.The quantum--like representation algorithm (QLRA) was  introduced by A. Khrennikov (1997) to solve the ``inverse Born's rule problem'', i.e. to construct a representation of probabilistic data-- measured in any context of science-- and represent this data by a complex or more general probability amplitude which matches a generalization of Born's rule.The outcome from QLRA matches the formula of total probability with an additional trigonometric, hyperbolic or hyper-trigonometric interference term and this is in fact a generalization of the familiar formula of interference of probabilities. We study representation of statistical data (of any origin) by a probability amplitude in a complex algebra and a Clifford algebra (algebra of hyperbolic numbers). The statistical data is collected from measurements of two dichotomous and trichotomous observables respectively. We see that only special statistical data (satisfying a number of nonlinear constraints) have a quantum--like representation. We also study simulations of quantum computers on classical computers.Although it can not be denied that great progress have been made in quantum technologies, it is clear that there is still a huge gap between the creation of experimental quantum computers and realization of a quantum computer that can be used in applications. Therefore the simulation of quantum computations on classical computers became an important part in the attempt to cover this gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation.  The second part of this thesis is devoted to adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulations on classical computers. Concretely we represent Simon's algorithm, Deutsch-Josza algorithm, Shor's algorithm, Grover's algorithm and quantum error-correcting codes in the Mathematica symbolic language. We see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include future algorithms in this framework.