Asymptotically good bosonic Fock state codes: Exact and approximate

2026-03-16

AI Summary

This work addresses the problem of exact and approximate quantum error correction for multimode Fock-state encodings under amplitude damping noise, particularly random photon loss. By introducing a truncated formalism of the amplitude damping channel, the study establishes an equivalence between exact and approximate correction within the Fock-state encoding framework. Leveraging constructions of classical codes with large minimum distance under the ℓ₁ metric, the authors design asymptotically good Fock-state codes with bounded photon number per mode. These codes further yield asymptotically optimal permutation-invariant qudit codes and kernel subspace codes. The resulting code family exhibits long coherence times, low sensitivity to photon loss, and high error-correcting capability, offering significant theoretical and practical advantages.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We examine exact and approximate error correction for multi-mode Fock state codes protecting against the amplitude damping noise. Based on a new formalization of the truncated amplitude damping channel, we show the equivalence of exact and approximate error correction for Fock state codes against random photon losses. Leveraging the recently found construction method based on classical codes with large distance measured in the $\ell_1$ metric, we construct asymptotically good (exact and approximate) Fock state codes. These codes have an additional property of bounded per-mode occupancy, which increases the coherence lifetime of code states and reduces the photon loss probability, both of which have a positive impact on the stability of the system. Using the relation between Fock state code construction and permutation invariant (PI) codes, we also obtain families of asymptotically good qudit PI codes as well as codes in monolithic nuclear state spaces.

Problem

• Fock state codes
• amplitude damping noise
• error correction
• photon loss
• asymptotically good codes

Innovation

• Fock state codes
• amplitude damping noise
• asymptotically good codes
• permutation invariant codes
• bounded per-mode occupancy