Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

Understand

We present explicit expressions for the central piece of a variational method developed by Shi et al.

• which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states [1].
• In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation.
• Using this result we find a closed expression for the energy functional and its gradient of a general fermionic quantum many-body Hamiltonian.