# Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches

## Authors

Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, Artur F. Izmaylov

## Abstract

We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the 1-norm of their coefficients, which is associated with the quantum circuit complexity. It is derived that the lowest possible LCU 1-norm for a given Hamiltonian is half of its spectral range. This lowest norm decomposition is practically unattainable for general Hamiltonians; therefore, multiple practical techniques to generate LCU decompositions are proposed and assessed. A technique using symmetries to reduce the 1-norm further is also introduced. In addition to considering LCU in the Schrödinger picture, we extend it to the interaction picture, which substantially further reduces the 1-norm.

#### 4 comments

###### AKim

Also, what's the definition of a molecular structure Hamiltonian - basically N-particle system with Coulomb forces or something else?