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Paper 1
A four-dimensional toric code with non-Clifford transversal gates
Tomas Jochym-O'Connor, Theodore J. Yoder
- Year
- 2020
- Journal
- arXiv preprint
- DOI
- arXiv:2010.02238
- arXiv
- 2010.02238
The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical $\mathsf{CCCZ}$ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyper-diamond. This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical $X$ and $Z$ and only allows for the implementation of a transversal Clifford gate. This work further develops the established connection between topological dimension and transversal gates in the Clifford hierarchy, generalizing the known designs for the implementation of transversal $\mathsf{CZ}$ and $\mathsf{CCZ}$ in two and three dimensions, respectively.
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Localization of low-energy eigenfunctions in Seba billiards
Minjae Lee
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7077
- arXiv
- 1407.7077
We investigate localization of low-energy modes of the Laplacian with a point scatterer on a rectangular plate. We observe that the point scatterer acts as a barrier confining the low-level modes to one side of the plate while assuming the Dirichlet boundary condition at a point does not induce this type of localization. This low-energy phenomenon extends to higher modes as we increase the eccentricity of the plate.
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