Clifford algebras, Spin groups and qubit trees

Abstract

Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan--Wigner construction also may be formally obtained in this approach by bringing the process up to trivial qubit chain (trunk). The methods can also be used for effective simulation of some quantum circuits corresponding to the binary tree structure. The modeling of more general qubit trees, as well as the relationship with the mapping used in the Bravyi--Kitaev transformation, are also briefly discussed.

16 pages, 9 figures

References in corpus (4)

• Lowering qubit requirements for quantum simulations of fermionic systems
• Quantum codes for quantum simulation of Fermions on a square lattice of qubits
• Transfer of arbitrary two qubit states via a spin chain
• Jordan-Wigner transformations for tree structures

Cited by in corpus (8)

• The Variational Quantum Eigensolver: a review of methods and best practices
• The Bonsai algorithm: grow your own fermion-to-qubit mapping
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Parallelization techniques for quantum simulation of fermionic systems
• On Classical Simulation of Quantum Circuits Composed of Clifford Gates
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables