Quantum computers have the potential to solve problems that are believed to be classically intractable. However, building such a device is proving to be very challenging. In this thesis, two physically promising settings for quantum computation are investigated: the one-way quantum computer and ancilla-based quantum gates. The majority of both the theoretical and experimental focus in the field of quantum computation has been on computation using 2-level quantum systems, known as qubits. In contrast to this, in this thesis I consider the relatively less well-understood setting of quantum computation using continuous variables or d-level quantum systems, called qudits. I develop a simple notation that encompasses each different encoding, and is applicable to a `general quantum variable'. These ideas are then used to investigate computational depth (a proxy for time) in quantum circuits and one-way quantum computations in this general quantum variable setting. In doing so, the parallelism inherent in the one-way quantum computer is made precise. In the second half of this thesis, a range of techniques are proposed for implementing entangling gates on a well-isolated computational register via interactions with `ancillary' systems. In particular, ancilla-based quantum gates for general quantum variables are investigated - including the interesting case of hybrid quantum computation, whereby more than one encoding is used in tandem. The methods proposed herein each have their own unique advantages, such as: reducing gate-counts in certain circuits, allowing for inherently parallel computation, or minimising the physical requirements for universal quantum computation. In particular, the final gate techniques that are proposed in this thesis may implement any quantum computation using only a single fixed ancilla-register interaction gate and ancillas prepared in simple states. This then allows the computational register to consist of well-isolated `memory' quantum variables and the ancillas need only be optimised for a single high-quality fixed interaction gate. Hence, this provides a simple and highly promising setting for physically implementing a quantum computer
