Bosonic quantum computing with near-term devices and beyond

Doctoral thesis, 2025

This thesis investigates scalable strategies for fault-tolerant quantum computation by developing and analyzing bosonic quantum codes, quantum low-density parity-check (LDPC) codes, and decoding protocols that aim to unify bosonic and discrete-variable quantum error correction.

In the continuous-variable regime, we explore the use of native nonlinearities in superconducting microwave circuits to realize a universal gate set for continuous-variable quantum computing, including the deterministic generation of a cubic phase state.
Separately, we propose and analyze the dissipatively squeezed cat qubit, a noise-biased bosonic encoding that offers improved error suppression and faster gate implementations compared to standard cat qubits.
To evaluate the broader viability of bosonic encodings, we study the performance of rotation-symmetric and Gottesman-Kitaev-Preskill (GKP) codes under realistic noise and measurement models, revealing important trade-offs in measurement-based approaches.

Recognizing the need to integrate bosonic codes into larger fault-tolerant architectures, we develop decoding techniques that explicitly leverage analog syndrome information from the readout of bosonic modes. These methods reduce the need for repeated measurements and enable quasi-single-shot decoding in concatenated schemes, forming a bridge between continuous-variable encodings and discrete-variable stabilizer codes.

To advance scalable discrete-variable fault tolerance, we introduce localized statistics decoding, a flexible and highly parallelizable decoding framework for general quantum LDPC codes with state-of-the-art accuracy.
Based on a novel on-the-fly matrix elimination strategy, this decoder efficiently identifies and resolves local error configurations, enabling low-latency and hardware-friendly implementations.
Additionally, we present quantum radial codes, a new family of single-shot quantum LDPC codes constructed from lifted products of classical quasi-cyclic codes.
These codes offer low overhead, tunable parameters, and competitive performance under circuit-level noise, making them promising candidates for near-term implementation.

Finally, we propose the concept of fault complexes, a homological framework for representing and analyzing faults in dynamic quantum error correction protocols. Extending the role of homology in static CSS codes, fault complexes provide a general language for the design and analysis of fault-tolerant schemes.