Local Jordan-Wigner transformations on the torus

TL;DR

This paper introduces a local unitary transformation from fermionic systems to qubits on a 2D torus, preserving locality and topological sectors, and extends previous work by explicitly constructing an intertwiner as a projected entangled pair operator.

Contribution

It provides a new locality-preserving unitary mapping that accounts for topological sectors and boundary conditions on a 2D torus, extending prior methods.

Findings

Constructed an explicit intertwiner as a projected entangled pair operator.

Encoded charge sectors and boundary conditions in ancillary qubits.

Achieved a unitary operator exchanging boundary conditions and charge sectors.

Abstract

We present a locality preserving unitary mapping from fermions to qubits on a 2D torus whilst accounting for the mapping of topological sectors. Extending the work of Shukla et al. [Phys. Rev. B 101, 155105], an explicit intertwiner is constructed in the form of a projected entangled pair operator. By encoding the information about the charge sectors (and if applicable the twisted boundary conditions) in ancillary qubit(s), the intertwiner becomes a unitary operator which exchanges boundary conditions and charge sectors.