Quantum

Stellar Representation of Gottesman Kitaev Preskill States on the Double Discrete Cylinder

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 30/10/2026, 06:43:25 UTC.

Briefings

A new arXiv preprint (2610.37831v1) introduces covariant integral quantization on the double discrete cylinder phase space, enabling the calculation of Wigner and stellar distributions for GKP states. The study identifies that ideal GKP logical states have no zeros on this phase space, while superpositions and fine-tuned squeezed states exhibit infinitely many zeros, mirroring the vacuum's role in GKP simulation challenges.

Key points

• Covariant integral quantization is developed on the double discrete cylinder phase space with the torus as configuration space, yielding the Wigner distribution and stellar representation.
• Ideal Gottesman Kitaev Preskill (GKP) logical states have no zeros on the phase space, whereas superpositions and fine-tuned squeezed states have infinitely many zeros.

Context

GKP states are central to fault-tolerant quantum computing architectures but their quantum resources remain under investigation. This work provides a mathematical framework to analyze their representation on a specific phase space, highlighting how their zero distribution relates to simulation difficulty.

Limitations

The evidence is an untrusted arXiv preprint (2610.37831v1) with no experimental data, citations, or verification status. Results are theoretical and subject to future validation. The phase space definition and specific numerical values for zero locations are not fully quantified in the abstract.

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