Jordan-Wigner transformations for tree structures

Abstract

The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

References in corpus (19)

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• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
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Cited by in corpus (13)

• Partonic collinear structure by quantum computing
• Free fermions behind the disguise
• Characterization of solvable spin models via graph invariants
• Geometric Criterion for Solvability of Lattice Spin Systems
• Clifford algebras, Spin groups and qubit trees
• Exploring Light-Cone Distribution Amplitudes from Quantum Computing
• Scattering Amplitude from Quantum Computing with Reduction Formula
• Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Post-thermalization via information spreading in open quantum systems
• Local Jordan-Wigner transformations on the torus
• The Hilbert-space structure of free fermions in disguise
• Expanding the Class of Free Fermions via Twin-Collapse Methods
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree