Spin-free quantum computational simulations and symmetry adapted states

TL;DR

This paper introduces a spin-free quantum simulation approach using symmetry-adapted states, enabling efficient N-body state preparation and advancing quantum computational methods for molecular systems.

Contribution

It presents a novel spin-free simulation framework that employs symmetry projection techniques for preparing N-body states, expanding quantum simulation capabilities.

Findings

Demonstrated methods on molecular hydrogen and cyclopropenyl cation

First explicit approach to symmetry-adapted N-body state preparation

Enhances quantum simulation efficiency for symmetric systems

Abstract

The ideas of digital simulation of quantum systems using a quantum computer parallel the original ideas of numerical simulation using a classical computer. In order for quantum computational simulations to advance to a competitive point, many techniques from classical simulations must be imported into the quantum domain. In this article, we consider the applications of symmetry in the context of quantum simulation. Building upon well established machinery, we propose a form of first quantized simulation that only requires the spatial part of the wave function, thereby allowing spin-free quantum computational simulations. We go further and discuss the preparation of N-body states with specified symmetries based on projection techniques. We consider two simple examples, molecular hydrogen and cyclopropenyl cation, to illustrate the ideas. While the methods here represent adaptations of known quantum algorithms, they are the first to explicitly deal with preparing N-body symmetry-adapted states.