What does this research mean for the field?

Symmetry-fixed holonomies at the deep holes of square and hexagonal momentum lattices enable the creation of spectrally isolated qubit and qutrit manifolds in finite two-cycle photonic geometries. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To identify optimal symmetry-fixed holonomies that maximize spectral isolation in two-cycle photonic geometries for realizing protected qubit and qutrit manifolds.

September 8, 2026Quantum ReportsOpen Access

Symmetry-Fixed Holonomies and Spectral Isolationin Two-Cycle Photonic Geometries: A Square Parent Manifold for a Qubit and a Hexagonal Qutrit Manifold

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Authors

MPMichel PlanatCentre National de la Recherche Scientifique

Discussion

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Implication

Theoretical modeling demonstrates spectral isolation of qubit and qutrit manifolds in two-cycle photonic microring lattices, indicating viable architectures for coherent optical state engineering.

Key Points

To identify optimal symmetry-fixed holonomies that maximize spectral isolation in two-cycle photonic geometries for realizing protected qubit and qutrit manifolds.
Evaluated twisted Laplacian normalized zeta determinants and lowest twisted eigenvalues across rectangular, square, and hexagonal momentum lattices.
Designed a finite-device model consisting of an 8×8 microring lattice enclosed by two phase-controlled boundary seams at a 16 GHz coupling scale.
Conducted a four-channel sensitivity analysis assessing uniform holonomy offsets, seam phase inhomogeneity, amplitude mismatch, and thermal-crosstalk limits.
Square and hexagonal lattices produced fourfold and threefold manifolds with spectral gaps of 2κ² and 4κ²/3, displaying linear splitting under holonomy errors while centroids remained stationary.
The 8×8 square microring lattice achieved a 17.32 GHz shell gap and a 1.92 GHz doublet separation at a phase-coordinate offset of εu = 0.10 from the antiperiodic point.
A triangular-link configuration realized a threefold qutrit manifold isolated by an 18.11 GHz spectral gap.

Cite This Study

Michel Planat (2026) studied this question.

synapsesocial.com/papers/6a9fd7c658e84d0ff5b46bc9 https://doi.org/10.3390/quantum8030088

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September 8, 2026Quantum ReportsOpen Access

Symmetry-Fixed Holonomies and Spectral Isolationin Two-Cycle Photonic Geometries: A Square Parent Manifold for a Qubit and a Hexagonal Qutrit Manifold

View Full Paper

Ask AI

Bookmark

Authors

MPMichel PlanatCentre National de la Recherche Scientifique

Discussion

Member takes

Implication

Theoretical modeling demonstrates spectral isolation of qubit and qutrit manifolds in two-cycle photonic microring lattices, indicating viable architectures for coherent optical state engineering.

Key Points

To identify optimal symmetry-fixed holonomies that maximize spectral isolation in two-cycle photonic geometries for realizing protected qubit and qutrit manifolds.
Evaluated twisted Laplacian normalized zeta determinants and lowest twisted eigenvalues across rectangular, square, and hexagonal momentum lattices.
Designed a finite-device model consisting of an 8×8 microring lattice enclosed by two phase-controlled boundary seams at a 16 GHz coupling scale.
Conducted a four-channel sensitivity analysis assessing uniform holonomy offsets, seam phase inhomogeneity, amplitude mismatch, and thermal-crosstalk limits.
Square and hexagonal lattices produced fourfold and threefold manifolds with spectral gaps of 2κ² and 4κ²/3, displaying linear splitting under holonomy errors while centroids remained stationary.
The 8×8 square microring lattice achieved a 17.32 GHz shell gap and a 1.92 GHz doublet separation at a phase-coordinate offset of εu = 0.10 from the antiperiodic point.
A triangular-link configuration realized a threefold qutrit manifold isolated by an 18.11 GHz spectral gap.

Cite This Study

Michel Planat (2026) studied this question.

synapsesocial.com/papers/6a9fd7c658e84d0ff5b46bc9 https://doi.org/10.3390/quantum8030088

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