Ternary-tree fermion-into-qubit code[1]
Description
A fermion-into-qubit encoding defined on ternary trees that maps Majorana operators into Pauli strings of weight \(\lceil \log_3 (2n+1) \rceil\).Gates
Fermion permutations on \(N\) modes can be done with a circuit of depth order \(O(\log^2 N)\) [2].Cousin
- Bravyi-Kitaev transformation (BKT) code— The ternary-tree fermion-into-qubit code improves over the BKT code by a factor of \(\approx 1.58\) in the weight of encoded fermionic operators [1].
Member of code lists
Primary Hierarchy
Parents
Ternary-tree fermion-into-qubit code
References
- [1]
- Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, “Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning”, Quantum 4, 276 (2020) arXiv:1910.10746 DOI
- [2]
- N. Constantinides, J. Yu, D. Devulapalli, A. Fahimniya, L. Schaeffer, A. M. Childs, M. J. Gullans, A. Schuckert, and A. V. Gorshkov, “Low-depth fermion routing without ancillas”, (2025) arXiv:2510.05099
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-03-20)
Cite as:
“Ternary-tree fermion-into-qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/ternary_tree_fermion, arXiv:2606.11484