Local Jordan-Wigner transformations on the torus
arXiv:2404.07727 · doi:10.1103/PhysRevB.111.115126
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.
arXiv comment5 pages, many figures, comments welcome
References in corpus (27)
- Fermionic quantum computation
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Mapping local Hamiltonians of fermions to local Hamiltonians of spins
- Gauging quantum states: from global to local symmetries in many-body systems
- Coexistence of superconductivity with partially filled stripes in the Hubbard model
- Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
- A Compact Fermion to Qubit Mapping
- Fermionic Matrix Product States and One-Dimensional Topological Phases
- Operator Locality in Quantum Simulation of Fermionic Models
- Fermions without fermi fields
- Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
- Local spin operators for fermion simulations
- Eliminating fermionic matter fields in lattice gauge theories
- Dualities in one-dimensional quantum lattice models: topological sectors
- Bosonization in three spatial dimensions and a 2-form gauge theory
- Bose-Fermi Transformation In Three Dimensional Space
- Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
- Quantum codes for quantum simulation of Fermions on a square lattice of qubits
- Majorana loop stabilizer codes for error correction of fermionic quantum simulations
- Exact bosonization in arbitrary dimensions
- Equivalence between fermion-to-qubit mappings in two spatial dimensions
- The Bonsai algorithm: grow your own fermion-to-qubit mapping
- Jordan-Wigner transformations for tree structures
- Discovering optimal fermion-qubit mappings through algorithmic enumeration
- Ultrafast Hybrid Fermion-to-Qubit mapping
- A tensor network approach to 2D bosonization