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

Abstract

We present explicit expressions for the central piece of a variational method developed by Shi et al (2018 Ann. Phys. 390 245) which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states. 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. We present a simple gradient-descent-based algorithm that can be used as an optimization subroutine in combination with imaginary time evolution, which by construction guarantees a monotonic decrease of the energy in each iteration step. Due to the simplicity of the quantum circuit implementing the variational state ansatz, the results of the algorithms discussed here and in Shi et al’s work could serve as an improved, beyond mean-field initial state in quantum computation.

Compressing Many-Body Fermion Operators under Unitary Constraints

“…Without approximate coupled-cluster initial state ADAPT fails to converge to the ground state for triplet O 2 . Although unitary compression presents a nice starting point, it is important to note that k = 1 k -uCJ, which is an instance of a Fermionc non-Gaussian state, is efficiently simulatable , and also provides a low-depth route for improving the starting state for ADAPT-VQE. We further note that it may be beneficial to study unitary compression for implementing dynamics of the generate determined from the gradient estimation step of ADAPT-VQE, which would implement a many-body step instead of implementing a single ADAPT term, which scales linearly with arbitrary qubit topology, or many-adapt terms, which would require Trotterization.…”