Linear-optical quantum computation with arbitrary error-correcting codes

Abstract

High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties, compatible with arbitrary codes and Gottesman-Kitaev-Preskill qubits on generic lattices, and featuring a natural way to leverage physical noise bias. Simulations of hyperbolic surface codes and bivariate bicycle codes, promising families of quantum low-density parity-check codes, reveal a threshold comparable to the 2D surface code with substantially better encoding rates.

20 pages, 4 figures, comments welcome

References in corpus (11)

• High-threshold and low-overhead fault-tolerant quantum memory
• Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
• Foliated Quantum Codes
• Matrix decompositions in Quantum Optics: Takagi/Autonne, Bloch-Messiah/Euler, Iwasawa, and Williamson
• Generation of Flying Logical Qubits using Generalized Photon Subtraction with Adaptive Gaussian Operations
• The role of entropy in topological quantum error correction
• Biased Gottesman-Kitaev-Preskill repetition code
• Qubit-oscillator concatenated codes: decoding formalism & code comparison
• Weight Reduced Stabilizer Codes with Lower Overhead
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
• Equivalent noise properties of scalable continuous-variable cluster states

Cited by in corpus (5)

• Quantum error correction for long chains of trapped ions
• Single-shot and measurement-based quantum error correction via fault complexes
• End-to-end switchless architecture for fault-tolerant photonic quantum computing
• Logical channel for heralded and pure loss with the Gottesman-Kitaev-Preskill code
• Logical channels in approximate Gottesman-Kitaev-Preskill error correction