Tiger surface code[1]
Description
A tiger-code family constructed from a hypergraph product of two repetition codes over the integers, rather than from concatenating a cat code with a qubit surface code. The code is conjectured to realize phases of \(U(1)\) gauge theory.
An \(r \times (2m-1)\) lattice encodes a logical qubit into \(2rm-r\) bosonic modes with \(d_X=m\) and \(d_Z \geq 4rm\sin^2\!\left(\frac{\pi}{2m}\right)\) [1]. The \(m=2\) case is the liger (long-tiger) surface code, which has \(d_X=2\) and \(d_Z=4r\).
Protection
The code corrects at least \(\lfloor (m-1)/2 \rfloor\) losses on arbitrary modes, and it detects pure-loss error patterns of total weight up to \(2m-2\) [1]. Its Euclidean distance obeys \begin{align} 4rm\sin^2\!\left(\frac{\pi}{2m}\right)\leq d_Z \leq 4rm\sin^2\!\left(\frac{\pi}{2m}\right)+4\sum_{j=1}^{m-1}\sin^2\!\left(\frac{(m-j)\pi}{m}\right) \tag*{(1)}\end{align} so choosing \(r=\Omega(m^2)\) makes both \(d_X\) and \(d_Z\) grow with system size. For suitable nonzero syndrome choices, the liger surface code has exact orthogonality in both logical \(X\)- and \(Z\)-bases at arbitrary energy [1].Cousins
- Compactified \(\mathbb{R}\) gauge theory code— Both the compactified \(\mathbb{R}\) gauge theory and tiger surface code are constructed from a hypergraph product of two repetition codes over the integers.
- Abelian topological code— The tiger surface code is conjectured to realize phases of \(U(1)\) gauge theory.
- Modular-qudit surface code— The tiger surface code can be thought of as a realization of the \(q\to\infty\) \(U(1)\) rotor limit [2] of the qudit surface code as a tiger code.
- Hypergraph product (HGP) code— The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.
- Repetition code— The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.
Member of code lists
Primary Hierarchy
Parents
The tiger surface code is constructed from a hypergraph product of two repetition codes over the integers.
Tiger surface code
References
- [1]
- Y. Xu, Y. Wang, C. Vuillot, and V. V. Albert, “Letting the Tiger out of Its Cage: Bosonic Coding without Concatenation”, Physical Review X 15, (2025) arXiv:2411.09668 DOI
- [2]
- V. V. Albert, S. Pascazio, and M. H. Devoret, “General phase spaces: from discrete variables to rotor and continuum limits”, Journal of Physics A: Mathematical and Theoretical 50, 504002 (2017) arXiv:1709.04460 DOI
Page edit log
- Victor V. Albert (2024-12-04) — most recent
Cite as:
“Tiger surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/tiger_surface