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Abstract
Quantum computers can potentially revolutionize computational science and technology, but their fullscale realization has proven to be an enormous challenge. A central issue is that noise severely limits the performance of quantum computers. To make quantum computers fault tolerant, quantum errorcorrection protocols are needed. A promising type of quantum error correction is bosonic error correction in which each qubit is encoded into the continuous variables of a bosonic mode. Experimental progress over the past two decades has enabled a high degree of control over several continuousvariable quantum systems, making bosonic codes a promising direction towards fault tolerance.
In this thesis, I investigate two prominent groups of continuousvariable quantum systems and propose novel schemes for quantum state generation and manipulation in these systems, with a primary focus on bosonic error correction.
The first group is optics, in which Gaussian operations across a large number of modes can be easily implemented. Optical platforms thus have many favorable features in terms of scalability and control, but losses constitute a central challenge. While losses can in principle be mitigated with bosonic quantum errorcorrecting codes, implementing these codes with available techniques is nontrivial. Here, I present schemes to optically generate and perform error correction on cat codes through linear optics and photon counting. Furthermore, I propose a method to generate GottesmanKitaevPreskill (GKP) states using a cavity quantum electrodynamics system as a nonGaussian resource. Finally, I show that, contrary to common belief, the cubic phase gate is not a suitable resource for nonClifford operations of GKP states.
The second group consists of systems in which strong bosonqubit couplings allow for the efficient implementation of conditional displacement gates. With current technology, this includes trapped ions and microwave cavity modes coupled to superconducting circuits. Here, I present and analyze improved protocols to generate and measure GKP states encoded in such systems. Additionally, I present two more generalpurpose quantum continuousvariable algorithms. The first algorithm is a method to generate squeezed states in the absence of a squeezing Hamiltonian, by instead superimposing multiple coherent states in phase space. The second algorithm is a method to transfer arbitrary continuousvariable states into a discretevariable qubit register.
In summary, the protocols presented herein aim to facilitate and expand the possibilities for control of continuousvariable quantum systems with existing and nearfuture technology.
In this thesis, I investigate two prominent groups of continuousvariable quantum systems and propose novel schemes for quantum state generation and manipulation in these systems, with a primary focus on bosonic error correction.
The first group is optics, in which Gaussian operations across a large number of modes can be easily implemented. Optical platforms thus have many favorable features in terms of scalability and control, but losses constitute a central challenge. While losses can in principle be mitigated with bosonic quantum errorcorrecting codes, implementing these codes with available techniques is nontrivial. Here, I present schemes to optically generate and perform error correction on cat codes through linear optics and photon counting. Furthermore, I propose a method to generate GottesmanKitaevPreskill (GKP) states using a cavity quantum electrodynamics system as a nonGaussian resource. Finally, I show that, contrary to common belief, the cubic phase gate is not a suitable resource for nonClifford operations of GKP states.
The second group consists of systems in which strong bosonqubit couplings allow for the efficient implementation of conditional displacement gates. With current technology, this includes trapped ions and microwave cavity modes coupled to superconducting circuits. Here, I present and analyze improved protocols to generate and measure GKP states encoded in such systems. Additionally, I present two more generalpurpose quantum continuousvariable algorithms. The first algorithm is a method to generate squeezed states in the absence of a squeezing Hamiltonian, by instead superimposing multiple coherent states in phase space. The second algorithm is a method to transfer arbitrary continuousvariable states into a discretevariable qubit register.
In summary, the protocols presented herein aim to facilitate and expand the possibilities for control of continuousvariable quantum systems with existing and nearfuture technology.
Original language  English 

Publisher  Department of Physics, Technical University of Denmark 

Number of pages  156 
Publication status  Published  2021 
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 1 Finished

Continuous variable quantum codes for faulttolerant quantum information processing
Hastrup, J., Andersen, U. L., NeergaardNielsen, J. S., Gehring, T., Terhal, B. M. & van Loock, P.
01/09/2018 → 08/12/2021
Project: PhD