Ternary-tree fermion-into-qubit code

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

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Union stabilizer (USt) codeQECC Quantum

Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum

Fermion-into-qubit code

Parents

Fermion-into-qubit code

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, A. M. Childs, M. J. Gullans, A. Schuckert, and A. V. Gorshkov, “Simulating fermions with exponentially lower overhead”, (2025) arXiv:2510.05099

Page edit log

Victor V. Albert (2024-03-20) — most recent

Cite as:

“Ternary-tree fermion-into-qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/ternary_tree_fermion

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/fermion_into_qubit/ternary_tree_fermion.yml.