Description
A member of a family of BBS codes with weight-two (two-body) gauge generators designed to suppress errors in adiabatic quantum computation.
The codes consist of the family of \([[4k+2l, 2k, g, 2]]\) BBS codes for even numbers of logical qubits and the family of \([[4k+2l-2, 2k-1, g, 2]]\) BBS codes for odd numbers of logical qubits, where \(k\) and \(l\) are integers satisfying \(l \leq \lceil (m-1)/2 \rceil\) with \(m\) either \(2k+1\) or \(2k\).
Gates
Single-qubit and two-qubit logical operators are two-local.
Parents
Child
- \([[6,2,3,2]]\) BBS code — The even-logical-qubit trapezoid family at \(l=k=1\) reduces to the \([[6,2,3,2]]\) BBS code.
Cousins
- \([[2m,2m-2,2]]\) error-detecting code — The trapezoid code family can be obtained from the \([[2m,2m-2,2]]\) error-detecting code by using some logical qubits as gauge qubits and imposing a two-dimensional qubit geometry [2].
- \([[6r,2r,2]]\) Ganti-Onunkwo-Young code — The even-logical-qubit trapezoid family at \(l=k\) is a subsystem version of the Ganti-Onunkwo-Young code [1].
- Small-distance block quantum code
References
- [1]
- M. Marvian and S. Lloyd, “Robust universal Hamiltonian quantum computing using two-body interactions”, (2019) arXiv:1911.01354
- [2]
- P. Singkanipa, Z. Xia, and D. A. Lidar, “Families of \(d=2\) 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions”, (2024) arXiv:2412.06744
Page edit log
- Victor V. Albert (2024-12-13) — most recent
Cite as:
“Trapezoid subsystem code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/trapezoid