Fermion-qubit mapping

Electron is a fermion, so electronic systems are described by Hamiltonians consisting of fermionic operator ${a_0, a_0^\dagger, ...}$ in the second quantization formalism. Since quantum computers are made up of qubits, one has to transform such Hamiltonians into the qubit operators ${X_0, Y_0, Z_0, ...}$ to treat them. There are several proposals to map the fermionic operators to the qubits operators.

Jordan-Wigner Transformation

Jordan-Wigner transformation is one of the most popular methods to transform fermionic operators to qubits operators. For details, please see Wikipedia's article.

Bravyi-Kitaev Transformation

Bravyi-Kitaev transformation has an advantage over Jordan-Wigner transformation in that a single electron operator $a_i, a_i^\dagger$ is mapped to qubit operators consisting of at most $\log(n)$ operators in $n$ qubit system, while Jordan-Winger transformation does so at most $n$ operators. Details are found here and reference therein.