Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation

TL;DR

This paper evaluates different Hamiltonian partitioning strategies for simulating electronic structures on quantum computers using Trotterization, highlighting trade-offs between accuracy and computational cost.

Contribution

It systematically compares fermionic and qubit-based Hamiltonian partitioning techniques, demonstrating how symmetry considerations reduce Trotter errors.

Findings

Fermionic partitioning yields lower Trotter errors due to symmetry use.

Qubit-based methods are more cost-effective despite higher errors.

Symmetry exploitation significantly improves simulation accuracy.

Abstract

Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via Trotterization, where a sequence of short-time evolutions of fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is used. Given multiple choices of possible Hamiltonian decompositions to fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends on the choice of the fragments. We assess efficiency of multiple Hamiltonian partitioning techniques using fermionic and qubit algebras for the Trotterization. Use of symmetries of the electronic Hamiltonian and its fragments significantly reduces the Trotter error. This reduction makes fermionic-based partitioning Trotter errors lower compared to those in qubit-based techniques. However, from the simulation-cost standpoint, fermionic methods tend to introduce quantum circuits with a greater number of T-gates at each Trotter step and thus are more computationally expensive compared to their qubit counterparts.