Bosonic quantum computing with near-term devices and beyond

TL;DR

This thesis advances scalable fault-tolerant quantum computing by developing bosonic and LDPC codes, decoding protocols, and analyzing implementations in superconducting microwave systems, bridging continuous and discrete-variable error correction.

Contribution

It introduces new bosonic codes, decoding methods exploiting analog information, and a homological framework for fault analysis, enhancing fault-tolerance and scalability in quantum computing.

Findings

Noise-biased bosonic encoding improves error suppression.

Decoding methods exploiting analog syndrome information enable quasi-single-shot decoding.

Quantum radial codes offer low-overhead, high-performance LDPC codes.

Abstract

(Abridged.) This thesis investigates scalable fault-tolerant quantum computation through the development of bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error correction. We investigate superconducting microwave implementations of continuous-variable quantum computing, including the deterministic generation of cubic phase states, and introduce the dissipatively stabilized squeezed cat qubit, a noise-biased bosonic encoding with enhanced error suppression and faster gates. The performance of rotation-symmetric and GKP codes is analyzed under realistic noise and measurement models, revealing key trade-offs in measurement-based schemes. To integrate bosonic codes into larger architectures, we develop decoding methods that exploit analog syndrome information, enabling quasi-single-shot decoding in concatenated systems. On the discrete-variable side, we introduce localized statistics decoding, a highly parallelizable decoder for quantum LDPC codes, and propose quantum radial codes, a new family of single-shot LDPC codes with low overhead and strong circuit-level performance. Finally, we present fault complexes, a homological framework for 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.