Construction of Superposition States of Energy Eigenstates via Classically Emulated Digital Quantum Simulation: The Hydrogen Molecule as an Example

TL;DR

This paper demonstrates how to construct superposition states of hydrogen molecule energy eigenstates using classically emulated digital quantum simulation, employing twirling operations and controlled unitaries, verified through observable calculations.

Contribution

It introduces a method to generate superposition states of molecular energy eigenstates via classically emulated quantum simulation, including the use of twirling and controlled unitaries.

Findings

Successfully generated superposition states of hydrogen molecule

Verified superposition states through observable matrix elements

Demonstrated feasibility of classically emulated quantum state construction

Abstract

We construct superposition states of energy eigenstates of the hydrogen molecule using classically emulated digital quantum simulation. We generate the ground state and excited states of the system via the twirling operation method, and construct superposition states of the ground state and an excited state of the system by applying a controlled excitation unitary transformation on the ground state with one ancillary qubit as the control. To verify the correctness of the resulting superposition state, we calculate matrix elements of several physical observables.