Work

Fiber Bundle Fault Tolerance of GKP Codes

Year: 2025

Type: article

Abstract: We investigate multi-mode GKP (Gottesman–Kitaev–Preskill) quantum error-correcting codes from a geometric perspective. First, we construct their moduli space as a quotient of groups and exhibit it as a fiber bundle over the moduli space of symplectically integral lattices. We then establish the Gottesman–Zhang conjecture for logical GKP Clifford operations, showing that all such gates arise from parallel transport with respect to a flat connection on this space. Specifically, non-trivial Clifford operations correspond to topologically non-contractible paths on the space of GKP codes, while logical identity operations correspond to contractible paths.

Source: Quantum

DOI: 10.22331/q-2025-10-29-1899

Authors: Ansgar G. Burchards, Steven T. Flammia, Jonathan Conrad

Institutions: Freie Universität Berlin, Phasecraft Inc. (United States), Virginia Tech, Helmholtz-Zentrum Berlin für Materialien und Energie

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $215

Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung