Quantum Error Correction and Simulation in Open Bosonic Systems

Quantum computers have the potential to surpass conventional computing, but they are hindered by noise which induces errors that ultimately lead to the loss of quantum information. This necessitates the development of quantum error correction strategies for large-scale quantum information processors.Bosonic quantum codes offer a promising solution, enabling quantum error correction on redundantly encoded information in a quantum harmonic oscillator. Two of the main sources of errors encountered in bosonic systems are photon loss and dephasing.Multiple bosonic quantum codes have been proposed and experimentally realized in the recent past.However, devising hardware-efficient bosonic quantum codes that are able to correct photon loss and dephasing to consistently enhance the life-time of logical quantum information beyond break-even, is a pressing problem in the scientific community.The cat code is a promising candidate as a biased-noise qubit, being able to correct well against dephasing errors, but it suffers from loss errors.In this thesis, we propose the squeezed cat code as way to simultaneously correct for photon loss and dephasing errors.We provide a full numerical and analytical analysis of the squeezed cat code, including protocols for encoding, quantum gates, error characterization, and an optimized recovery procedure suitable for implementation on current quantum hardware platforms.Through numerical simulations using realistic parameters, we demonstrate that even moderate squeezing enables the squeezed cat code to significantly outperform the conventional cat code in correcting particle loss errors. Notably, the squeezed cat code improves resilience to dephasing errors at the same time, enhancing the noise bias of logical error errors.Our main motivation lies in the fact that as squeezing is a Gaussian operation, the generation and manipulation of the squeezed cat code can be achieved through quadratic operations, without the need to introduce higher-order processes.To simulate the dynamics of driven-dissipative bosonic systems accurately and efficiently, with bosonic codes in mind specifically, new numerical methods need to be developed. For bosonic codes, tailored numerical methods can enable the study of leakage out of the code space, effects of time-dependent and noisy gate operations, or dissipative phase transitions.The second part of this thesis addresses this problem by focusing on a new variational approach for efficiently simulating the dynamics of open interacting many-boson quantum systems. The method uses an ansatz for the density matrix expanded in a basis of photon-added coherent states. This makes it well-suited for driven-dissipative systems where the state exhibits quantum fluctuations on top of a displaced field, enabling the simulation of multiple coupled modes with large occupation numbers that pose a challenge for Fock-space methods. Several example simulations are provided that validate the method and illustrate its potential for predictively modeling interacting bosonic systems.We further extend this method to include the rotational symmetry of cat qubits and showcase the efficient simulation of cat qubit dynamics.Taken together, this thesis presents important theoretical and computational advancements towards realizing and simulating hardware-efficient bosonic quantum codes required for scalable and fault-tolerant quantum information processing.