Continuous-variable quantum codes for fault-tolerant quantum information processing

Quantum computers can potentially revolutionize computational science and technology, but their full-scale 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 error-correction 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 continuous-variable quantum systems, making bosonic codes a promising direction towards fault tolerance.

In this thesis, I investigate two prominent groups of continuous-variable 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 error-correcting codes, implementing these codes with available techniques is non-trivial. 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 Gottesman-Kitaev-Preskill (GKP) states using a cavity quantum electrodynamics system as a non-Gaussian resource. Finally, I show that, contrary to common belief, the cubic phase gate is not a suitable resource for non-Clifford operations of GKP states. The second group consists of systems in which strong boson-qubit 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 general-purpose quantum continuous-variable 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 continuous-variable states into a discrete-variable qubit register. In summary, the protocols presented herein aim to facilitate and expand the possibilities for control of continuous-variable quantum systems with existing and near-future technology.