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Abstract
In measurementbased quantum computation (MBQC), or cluster state computation, gates are implemented on a multimode 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 twodimensional (2D) cluster state is proposed and experimentally demonstrated. Assuming the availability of GottesmanKitaevPreskill (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 faulttolerant computation are discussed. Finally, a new computation scheme is proposed where gates are implemented on a threedimensional cluster state allowing topological error correction. Taking finite squeezing in both the cluster state generation and approximate GKPstates into account, faulttolerant 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 twomode squeezed state generation in two spatial modes from a single timemultiplexed squeezed light source using optical switching and delay. In this demonstration, multiple experimental techniques are developed, including efficient freespace to fiber coupling, infiber phase control, and fiberbased homodyne detection, each of which plays important roles in the experimental demonstration of the following cluster state generation and gate implementation.
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 twodimensional (2D) cluster state is proposed and experimentally demonstrated. Assuming the availability of GottesmanKitaevPreskill (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 faulttolerant computation are discussed. Finally, a new computation scheme is proposed where gates are implemented on a threedimensional cluster state allowing topological error correction. Taking finite squeezing in both the cluster state generation and approximate GKPstates into account, faulttolerant 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 twomode squeezed state generation in two spatial modes from a single timemultiplexed squeezed light source using optical switching and delay. In this demonstration, multiple experimental techniques are developed, including efficient freespace to fiber coupling, infiber phase control, and fiberbased homodyne detection, each of which plays important roles in the experimental demonstration of the following cluster state generation and gate implementation.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Department of Physics, Technical University of Denmark 
Number of pages  179 
Publication status  Published  2021 
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 1 Finished

NonGaussian Cluster States
Larsen, M. V., Andersen, U. L., NeergaardNielsen, J. S., Huck, A., Lam, P. K. & Ralph, T. C.
Technical University of Denmark
01/10/2017 → 12/05/2021
Project: PhD