Bosonic coding: introduction and use cases
Victor V. Albert
TL;DR
The paper surveys bosonic coding as a framework for robust quantum information processing in continuous-variable CV systems, classifying codes into bosonic stabilizer codes and bosonic Fock-state codes. It details representative constructions such as GKP, GKP-stabilizer, cat, binomial, and number-phase codes, and discusses how infinite dimensionality enables error correction beyond DV limits, including continuous transversal gates and bias-preserving dynamics. It analyzes noise models—loss, dephasing, and displacement—and maps code performance to these channels, highlighting hardware efficiency gains and decoding strategies that leverage analog information. The work emphasizes practical implications for quantum memories and communications, including the capacity for Gaussian-displacement channels and the potential for integrating bosonic and DV approaches to achieve scalable fault-tolerant quantum computation with non-Gaussian resources like GKP states. It also points to open questions, such as thresholds for GKP-based schemes and the broader role of bosonic codes in quantum simulation and topological modeling.
Abstract
Bosonic or continuous-variable coding is a field concerned with robust quantum information processing and communication with electromagnetic signals or mechanical modes. I review bosonic quantum memories, characterizing them as either bosonic stabilizer or bosonic Fock-state codes. I then enumerate various applications of bosonic encodings, four of which circumvent no-go theorems due to the intrinsic infinite-dimensionality of bosonic systems.