Global fermionic mode optimization via swap gates

TL;DR

This paper introduces a method for optimizing fermionic modes globally in quantum many-body wave functions using swap gates, improving representations for complex systems.

Contribution

It presents a novel approach combining Grassman manifold optimization with swap gates for better fermionic mode representation.

Findings

Effective in large-scale DMRG simulations

Improves representation of strongly correlated systems

Applicable to 2D fermionic lattice models

Abstract

We propose a general approach to find an optimal representation of a quantum many body wave function for a given error margin via global fermionic mode optimization. The stationary point on a fixed rank matrix product state manifold is obtained via a joint optimization on the Grassman manifold [Phys. Rev. Lett. 117, 210402] together with swap gates controlled permutations. The minimization of the global quantity, the block entropy area, guarantees that the method fulfills all criteria with respect to partial derivatives. Numerical results via large scale density matrix renormalization group simulations on strongly correlated molecular systems and two-dimensional fermionic lattice models are discussed.