---
# System prepended metadata

title: Is the Trotterized UCCSD Ansatz ChemicallyWell-Defined?
tags: [papers, Quantum Calculation]

---

###### tags: `papers` `Quantum Calculation`
# Is the Trotterized UCCSD Ansatz ChemicallyWell-Defined?

[arXiv:1910.10329](https://arxiv.org/abs/1910.10329)

## Abstract
Explore the effects of ordering on the Trotterized UCCSD ansatz and k-upCCGSD ansatz.
Different energy scale is observed among different ordering of operators. This paper suggests the need of not only the operators used but also order in which they appear.

## Introduction
The history of quantum chemistry calculations with quantum algorithms.

About NISQ devises.
* While quantum error correction, which use lots of qubits is not expected to be succesful in the near future, the potentials of NISQ devices which use few qubits are studied.
* VQE provides the path of NISQ devises which limits the depth of circuits. 

About UCCSD ansatz.
* Usefullness
* Explanations

## Numerical examples
Calculated the ground energy of several molcules (LiH, H$_6$, BeH$_2$, and N$_2$) with 1s and 2s orbital frozen.
* basis sto-3g
* Mapping = jordanwigner
* Optimizer BFGS

Comparion with potential curves with UCCSD, SGO, random shuffled, and FCI.
> In the papaer says UCCSD has several ways of ordering e.g. SGO, random shuffled, though I think there are no definions written in the paper.
> Un-trotter ansatz iin the paper may refer to the UCCSD and the SGO?

![](https://i.imgur.com/1solfgM.png)

## k-upCCGSD
The UCCSD ansatz seemed to be accurate when the number of operator which are not related to the accurate estimates. These operators are seemed to have a role on minimizeing the differences between the ordering.

To test this considerd compared k-upCCGCD. 

![](https://i.imgur.com/nQhVKi4.png)

## Conclusions
The ordering affects the simulation results.

Also suggests that there are symmetrical patterns that gives the lowest energy. 

