Continuous Variable Cluster State Computation

In measurement-based quantum computation (MBQC), or cluster state computation, gates are implemented on a multi-mode entangled cluster state by projective measurements. In the optical continuous variable (CV) regime, such cluster state can be deterministically generated while a class of measurements is efficiently implemented by homodyne detection. This immediately allows for the deterministic implementation of Gaussian gates in a scalable optical computation platform.

In this thesis, work towards the realization of CV MBQC is presented. In MBQC, a cluster state of at least two dimensions is required, and in this thesis, the generation of such two-dimensional (2D) cluster state is proposed and experimentally demonstrated. Assuming the availability of Gottesman-Kitaev-Preskill (GKP) encoded input qubits, a universal computation scheme for the2D cluster state is proposed, and noise analysis of the computation scheme is carried out and compared to other computation schemes on 2D cluster states. Following the proposed computation scheme, a universal Gaussian gate set is implemented on the generated cluster state by projective measurements, and to demonstrate the programmability, gates are combined into a small quantum circuit. Gate noise, caused by finite squeezing, is characterized, and the requirements for fault-tolerant computation are discussed. Finally, a new computation scheme is proposed where gates are implemented on a three-dimensional cluster state allowing topological error correction. Taking finite squeezing in both the cluster state generation and approximate GKP-states into account, fault-tolerant computation is shown to be possible by simulation when the squeezing level is above a certain squeezing threshold.

To aid the experimental implementations, the focus throughout this thesis is on temporal encoding where resources are reused in time minimizing the required spatial resources, i.e. time multiplexing. To this end, the thesis starts with a demonstration of two-mode squeezed state generation in two spatial modes from a single time-multiplexed squeezed light source using optical switching and delay. In this demonstration, multiple experimental techniques are developed, including efficient free-space to fiber coupling, in-fiber phase control, and fiber-based homodyne detection, each of which plays important roles in the experimental demonstration of the following cluster state generation and gate implementation.