Optimal quantum control beyond the minimal system

Quantum computing holds the potential to transform fields ranging from cryptography to materials science by tackling problems that exceed the reach of classical computation. Yet, moving beyond proof-of-concept demonstrations to practical large-scale quantum systems requires overcoming two major challenges: the exponential increase in control complexity as the number of qubits grows and the inherent fragility of quantum operations in realistic experimental conditions. While high-fidelity control of individual qubits has been demonstrated, scalable architectures demand protocols that maintain precision across thousands of qubits, even in the presence of imperfections. This thesis addresses these challenges through advances in quantum control and error resilience. First, we introduce a resource-efficient control framework that mitigates the exponential scaling of state-vector representations, enabling precise manipulation of many-qubit systems that were previously beyond reach. This approach supports the development of efficient protocols for state preparation and quantum simulation—both essential for realizing practical quantum technologies. Second, we develop error-mitigation strategies to suppress decoherence in multi-qubit arrays. Key contributions include shuttling protocols for trapped-ion systems that minimize motional heating during transport, noise-robust entangling gates that remain resilient to simultaneous frequency errors, initial motional excitation, and motional heating due to environmental coupling, as well as spectral engineering techniques that remove the need for mode selectivity and resolved sideband requirements in multi-ion operations. Together, these advances refine the control of large-scale qubit systems and provide concrete steps toward scalable, fault-tolerant quantum processors.