4.7. Fermion to qubit mappings
We consider a system of 
fermions, each labeled with an integer from 
to 
. We need a fermion to qubit mapping, a description of the correspondence between states of fermions and states of qubits, or, equivalently, between fermionic operators and multi-qubit operators. We need a mapping between the fermion creation and annihilation operators and multi-qubit operators. The Jordan-Wigner and the Bravyi-Kitaev transformations are widely used and simulate a system of electrons with the same number of qubits as electrons.
4.7.1. Qubit creation and annihilation operators
We define qubit operators that act on local qubits [Yepez] [Chiew], as shown in Figure 4.22:
Figure 4.22 – Qubit creation and annihilation operators
The qubit operators have the anti-commutation relation: 
.
4.7.2. Jordan-Wigner transformation
The Jordan-Wigner (JW) transformation stores the occupation of each spin orbital in each qubit. It maps...