Hessian QSC[1]
Description
Quantum spherical code encoding a logical qubit, with each codeword an equal superposition of vertices of a Hessian complex polyhedron. For the unit sphere, the codewords are \begin{align} |\overline{0}\rangle &= \frac{1}{\sqrt{27}}\left( \sum_{\mu,\nu=0}^{2} |0,\omega^{\mu},-\omega^{\nu}\rangle + |-\omega^{\nu},0,\omega^{\mu}\rangle + |\omega^{\mu},-\omega^{\nu},0\rangle \right) \tag*{(1)}\\ |\overline{1}\rangle &= \frac{1}{\sqrt{27}}\left( \sum_{\mu,\nu=0}^{2} |0,-\omega^{\mu},\omega^{\nu}\rangle + |\omega^{\nu},0,-\omega^{\mu}\rangle + |-\omega^{\mu},\omega^{\nu},0\rangle \right)~, \tag*{(2)}\end{align} where \(\omega = e^{\frac{2\pi i}{3}}\).
Protection
Parent
- Quantum spherical code (QSC) — The Hessian QSC is an example of a QSC with logical constellation built from the Hessian complex polyhedron.
Cousin
- Hessian polyhedron code — The Hessian QSC is the quantum generalization of the classical Hessian polyhedron code.
References
- [1]
- S. P. Jain et al., “Quantum spherical codes”, Nature Physics (2024) arXiv:2302.11593 DOI
Page edit log
- Victor V. Albert (2023-04-09) — most recent
- Shubham P. Jain (2023-04-08)
Cite as:
“Hessian QSC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/hessian_qsc