Bravyi-Kitaev transformation (BKT) code[1]
Description
A fermion-into-qubit encoding that maps Majorana operators into Pauli strings of weight \(\lceil \log (n+1) \rceil\). The code can be reformulated in terms of Fenwick trees [2], and the Pauli-string weight can be further optimized to yield the segmented Bravyi-Kitaev (SBK) transformation code [3].Cousins
- Jordan-Wigner transformation code— The weight of a Majorana operator in the BKT (JW transformation) code scales logarithmically (linearly) with \(n\), with the former demonstrating an exponential imporvement [4].
- Ternary-tree fermion-into-qubit 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 [4].
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Parents
Bravyi-Kitaev transformation (BKT) code
References
- [1]
- S. B. Bravyi and A. Yu. Kitaev, “Fermionic Quantum Computation”, Annals of Physics 298, 210 (2002) arXiv:quant-ph/0003137 DOI
- [2]
- P. M. Fenwick, “A new data structure for cumulative frequency tables”, Software: Practice and Experience 24, 327 (1994) DOI
- [3]
- V. Havlíček, M. Troyer, and J. D. Whitfield, “Operator locality in the quantum simulation of fermionic models”, Physical Review A 95, (2017) arXiv:1701.07072 DOI
- [4]
- 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
Page edit log
- Victor V. Albert (2024-03-20) — most recent
Cite as:
“Bravyi-Kitaev transformation (BKT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/bkt