Spin-1/2 Fermion Local Pair Encoding into Qubits: Application to the 2D-Block-Diagonal Geminal Ansatz
Abstract
Spin-1/2 Fermions, such as electrons are usually encoded into qubits through one-particle occupancy, parity or a mix of the two. Then, Fermionic operators have to be transformed into appropriate Pauli string acting on the qubits, according to Jordan-Wigner, Parity, or Bravyi-Kitaev transformations, respectively. In the present work, we study alternative encodings in terms of Fermionic pair occupancy and the associated operator transformations. Although the scaling of the general case is not favorable neither in terms of number of qubits nor in terms of Pauli operations, some subcases can be particularly suitable to capture the physics of certain systems such as molecular electrons, with a reduced number of qubits and with transformed ladder operators localized to blocks of a few qubits only. An application to the 2D-block diagonal geminal ansatz demonstrates the usefulness of the encoding. The treatment of several molecules shows the effectiveness of the ansatz.
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BibTeX
@misc{cassamchenai2026spin12,
title = {{Spin-1/2 Fermion Local Pair Encoding into Qubits: Application to the 2D-Block-Diagonal Geminal Ansatz}},
author = {Patrick Cassam-Chenaï and Louis Jourdan},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05734629v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Spin-1/2 Fermion Local Pair Encoding into Qubits: Application to the 2D-Block-Diagonal Geminal Ansatz
AU - Patrick Cassam-Chenaï
AU - Louis Jourdan
PY - 2026
DA - 2026/09/01
PB - HAL
UR - https://hal.science/hal-05734629v1
AB - Spin-1/2 Fermions, such as electrons are usually encoded into qubits through one-particle occupancy, parity or a mix of the two. Then, Fermionic operators have to be transformed into appropriate Pauli string acting on the qubits, according to Jordan-Wigner, Parity, or Bravyi-Kitaev transformations, respectively. In the present work, we study alternative encodings in terms of Fermionic pair occupancy and the associated operator transformations. Although the scaling of the general case is not favorable neither in terms of number of qubits nor in terms of Pauli operations, some subcases can be particularly suitable to capture the physics of certain systems such as molecular electrons, with a reduced number of qubits and with transformed ladder operators localized to blocks of a few qubits only. An application to the 2D-block diagonal geminal ansatz demonstrates the usefulness of the encoding. The treatment of several molecules shows the effectiveness of the ansatz.
ER -