Quantum computation algorithm for many-body studies

Understand

We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer.

• We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian, written as products of a given number of creation and annihilation operators, as input.
• To demonstrate the applicability of the algorithm, we calculate eigenvalues and eigenvectors of two model Hamiltonians, the well-known Hubbard model and a generalized pairing Hamiltonian.
• Extensions to other systems are discussed.