Fermionic Hamiltonians for quantum simulations: a general reduction scheme

TL;DR

This paper introduces an optimization scheme that reduces complex k-local fermionic Hamiltonians into simpler 2-local terms, preserving physical properties and enabling more feasible quantum simulations on current hardware.

Contribution

The authors propose a novel method to transform k-local fermionic Hamiltonians into 2-local terms with minimal coupling variation, improving upon perturbation-based approaches.

Findings

Reduces k-local terms to 2-local terms while conserving physical properties

Achieves smaller variation in coupling constants compared to existing methods

Facilitates implementation of fermionic simulations on current quantum hardware

Abstract

Many-body fermionic quantum calculations performed on analog quantum computers are restricted by the presence of k-local terms, which represent interactions among more than two qubits. These originate from the fermion-to-qubit mapping applied to the electronic Hamiltonians. Current solutions to this problem rely on perturbation theory in an enlarged Hilbert space. The main challenge associated with this technique is that it relies on coupling constants with very different magnitudes. This prevents its implementation in currently available architectures. In order to resolve this issue, we present an optimization scheme that unfolds the k-local terms into a linear combination of 2-local terms, while ensuring the conservation of all relevant physical properties of the original Hamiltonian, with several orders of magnitude smaller variation of the coupling constants.