# CVQE

**Repository Path**: QuContractor/CVQE

## Basic Information

- **Project Name**: CVQE
- **Description**: Quantum snake algorithm: Collective variational quantum eigensolvers for quantum chemistry
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-03-24
- **Last Updated**: 2020-12-19

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Quantum snake algorithm: 
* This is the source code for the paper: 

Dan-Bo Zhang and Tao Yin, Collective optimization for variational quantum eigensolvers, [Phys. Rev. A **101**, 032311(2020).](https://link.aps.org/doi/10.1103/PhysRevA.101.032311) ([arXiv: 1910.14030](https://arxiv.org/abs/1910.14030))

### Collective variational quantum eigensolvers (CVQE) for quantum chemistry

We propose a hybrid quantum-classical algorithm that can provide collective optimization for the VQE
to solve a group of related Hamiltonians more efficiently.

A brief introduction for VQE can be found in [QuContractor's github repository.](https://github.com/QuContractor/VQE_tutorial/)

### Simulate molecules with varied bond lengths



<img src="figs/fig1_1.jpg" alt="energies" style="zoom: 40%;" />

We simulated different molecules (H2, LiH, HeH+) with CVQE. Numeral simulations show that the CVQE exhibits clear collective behavior in the optimization process of updating parameters. 

The numerical simulations are mostly performed by using the [Huawei HiQ simulator framework](https://hiq.huaweicloud.com/). 

* The calculation for H2 can be found in [CVQE_H2](https://github.com/QuContractor/CVQE/blob/master/H2/snake_VQE_H2_pjq.ipynb), and [CVQE_H2 with IBM Qiskit](https://github.com/QuContractor/CVQE/blob/master/H2/snake_VQE_H2_IBM.ipynb)
* The calculation for LiH can be found in [CVQE_LiH](https://github.com/QuContractor/CVQE/blob/master/LiH/snake_VQE_LiH.ipynb)
* The calculation for HeH+ can be found in [CVQE_HeH+](https://github.com/QuContractor/CVQE/blob/master/HeH%2B/snake_VQE_HeH.ipynb)

### Avoid local minimum

<img src="figs/fig5.jpg" alt="local_mini" width = "500" />

The snake algorithm gives rise to collective motion of parameters of different tasks
that can avoid being trapped in local minimums. 

The example with H2 can be found in [CVQE_H2](https://github.com/QuContractor/CVQE/blob/master/H2/snake_VQE_H2_2theta.ipynb).

### Cite:

@article{PhysRevA.101.032311,
  title = {Collective optimization for variational quantum eigensolvers},
  author = {Zhang, Dan-Bo and Yin, Tao},
  journal = {Phys. Rev. A},
  volume = {101},
  issue = {3},
  pages = {032311},
  numpages = {8},
  year = {2020},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevA.101.032311},
  url = {https://link.aps.org/doi/10.1103/PhysRevA.101.032311}
}