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Mappings between fermions and qubits are valuable constructions in physics.
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The difference in sign introduce between the vertical up and down orientations is included to ensure that cycles around odd faces are equal to 1 1 and not − 1 -1
Cited in the paper.
See Supplemental Material at [URL will be inserted by publisher] for: explicit constructions of logical qubit operators in case (III) of the mapping; an example of a variant of the mapping tailored to hexagonal lattices; and a more explicit proof of the correctness of the compact mapping
Cited in the paper.
J † J = 𝕀 H 1 J^{\dagger}J=\mathbb{I}_{H_{1}} and J J † = Proj ( Image ( J ) ) JJ^{\dagger}=\textrm{Proj}(\textrm{Image}(J))
Cited in the paper.
Kanav Setia, Sergey Bravyi, Antonio Mezzacapo, and James D Whitfield, “Superfast encodings for fermionic quantum simulation,” Physical Review Research 1
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Zhang Jiang, Jarrod McClean, Ryan Babbush, and Hartmut Neven, “Majorana loop stabilizer codes for error mitigation in fermionic quantum simulations,” Phys. Rev. Applied 12
2019
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