Towards fault-tolerant quantum computing: Advanced techniques for error reduction,mitigation and their applications

Quantum computing holds the potential to address problems that are currently considered intractable for classical processors by leveraging quantum mechanical effects for simulation, optimization, and chemistry. Despite recent technological progress, quantum hardware remains in the noisy intermediate-scale regime, where coherence limits, gate imperfections, and readout errors restrict circuit depth and algorithmic reliability. Although first demonstrations of small-scale Quantum Error Correction exist, logical processors with low logical error rates are still distant. In the near term, even error-corrected qubits are expected to operate with residual error, which means that improving calibration and mitigating errors at the physical and circuit level will remain essential for obtaining meaningful results. Established calibration routines and mitigation methods such as Zero-Noise-Extrapolation (ZNE) are valuable, but need to be further improved and more rigorously validated with respect to their underlying assumptions, stability and quantitative benefits. This thesis addresses error reduction techniques on transmon qubits through calibration, gate analysis, and circuit-level mitigation. First, a systematic comparison of two single-qubit amplitude calibration techniques is carried out (cross-point and ping-pong calibration), followed by an analysis of two implementations of a two-qubit gate, based on the cross-resonance interaction. The results show that cross-point calibration offers faster convergence, higher precision and a more favorable signal to noise ratio than ping-pong calibration. Hamiltonian tomography confirms the validity of a reduced model for the cross-resonance interaction, and algorithmic tests reveal that direct and echoed CNOT gates offer complementary advantages depending on the application. Second, the thesis develops and evaluates the method of  Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE). Its main idea consists of measuring the effective error strength of a circuit through inverted circuits. This quantity is then used for extrapolation towards zero noise rather than relying on simple, approximate noise scaling assumptions as in standard ZNE.  This approach constitutes a novel and original method. IC-ZNE consistently produces results closer to ideal reference values than standard ZNE. The method achieves up to 77% error reduction in observable error on the tested circuits compared to standard ZNE and simple post processing filters can yield up to 39% reduction in selected cases compared to standard ZNE. Further refinements introduce noise-adaptive circuit scaling strategies that enhance mitigation outcomes without significant additional cost. The performance of these techniques is examined across several circuits and in the context of variational quantum algorithms. Applications to the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver demonstrate that these techniques extend the useful operating regime of current devices, although their effectiveness decreases for very deep circuits or unfavorable variational ansätze. Taken together, the calibration and mitigation techniques investigated and developed in this thesis demonstrate practical routes toward enhancing the reliability of near-term quantum processors. While they cannot replace full fault-tolerant quantum computation, they offer useful and complementary capabilities that support progress toward scalable quantum technologies.