Optimal Quantum Driving for Single-Qubit Gates

Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing