| Abstrakt: | The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm
widely investigated for near-term quantum hardware. Its performance depends criti-
cally on two components: the classical optimizer used to navigate the parameter space,
and the error mitigation techniques used to recover accurate energy estimates from
noisy quantum evaluations. This thesis applies the Harmonic Oscillator based Particle
Swarm Optimization (HOPSO) algorithm to VQE on the four-qubit hydrogen molecule
benchmark, and conducts a systematic empirical study of HOPSO under multiple noise
models and error mitigation strategies. Three depolarizing noise models spanning two
orders of magnitude in error probability are studied, alongside shot noise at multiple
measurement counts. Two error mitigation methods are evaluated: Zero-Noise Ex-
trapolation with three extrapolation schemes and two noise scaling approaches, and
Probabilistic Error Cancellation applied post-hoc. HOPSO is compared against three
established optimizers (PSO, DE, COBYLA) under the studied noise configurations,
and a representative IBM fake backend is used to validate the findings under realistic
device noise. The principal findings are that HOPSO recovers high-quality parameter
vectors under isolated depolarizing noise without any mitigation, that applying ZNE
during the optimization loop on this benchmark degrades the actual quality of found
parameters across all studied noise configurations, and that the relative ranking of opti-
mizers under combined gate and shot noise places Differential Evolution slightly above
HOPSO, with both above PSO. The conditions under which ZNE during optimization
is counterproductive on this benchmark are characterized empirically and contrasted
with the post-hoc application regime in which mitigation is typically evaluated in the
literature.
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