Classiq
Adaptive VQE for quantum chemistry - Paper Implementation Project
Research paper to implement
We (@Dacastillo , @DiegoTancara, and @jervaal) are trying to implement the next paper: Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry. This work was studied for us because it explores the capabilities of an adaptive VQE to improve the mistakes in the calculation of bonding energy for different atom pairs (a fundamental study on quantum chemistry).
An adaptive VQE differs from a regular VQE because it adds an adaptation process of the quantum gates needed to ansatz (unlike standard VQE where the ansatz is fixed), making the work with greater atoms easier. So, the Adaptive VQE goal is to find a different optimal circuit for each atom pair we need.
The implementation of his work would allow us to calculate a better approximation for bonding energy curves (which can be implemented on Classiq). This improvement could give better force curves derivations, which is very useful to make potential for ab initio molecular dynamics simulations (AIMD), as we suggested since this work.
Technical approach
The steps we must take for the development of the paper implementation are:
- Generalized implementation of VQE. Testing of VQE implementation in Classiq.
- Build the complete Adapt-VQE scheme, as the paper proposes. According to the paper, we would need to add more parameters to the system for variational circuit optimization.
- Implementation of noise methods, including methods recommended by the paper, such as depolarizing noise, among other possible noise sources.
Example with key concepts
The examples we could do, inspired by the paper used, are the implementation of all the code for the next pairs of atoms:
- H-H
- Li-H
- H-F
- H-Be-H
- H-H-H-H
All these examples will be compared and checked to find the best adjustment to the known experimental and computational data about these bonds. After that, these functions will be derived to build empirical potentials.
@Dacastillo, what paper? There is no link. In addition, please review other proposals for projects to understand the structure needed in order to get our approval.
@Dacastillo, what paper? There is no link. In addition, please review other proposals for projects to understand the structure needed in order to get our approval.
OK. No problem. I'm still editing. I will finish this during today, I believe.
Update: Now I am written a more complete version.
@TaliCohn: Now I completes The draft. What Is your opinión/comment? Greetings.
Thank you @Dacastillo , could you please provide more detail on how you will implement the noise methods? will you use Classiq for that?
Thank you for your question @TomerGoldfriend: Our first idea is to implement the noise methods following the idea that the paper to implement shows: Putting a single-qubit depolarising noise channel following the next equation (with its respective error probability p):
$$\mathcal{D}(i,p)[\rho]=(1-p)\rho+\frac{p}{3}\sum_{\sigma_i}\sigma_i\rho\sigma_i $$
and readout the result as a density matrix to improve the noise analysis. This kind of noise gate would be applied after the application of each two-qubit CNOT gate.
We pretend to simulate this gates using Classiq, implemented in Python scripts to combining this code with another libraries to complement the final analysis (like Openfermion or Scipy). In summary, we need Classiq to make more tractable the quantum computing part of the Adapt-VQE algorithm, and explore different noise implementations.
Greetings.
OK @Dacastillo , please note that currently we do not support density matrix simulator. Actually, we do not have an Adapt-VQE in our repo, so it will be nice to have this as part of your contribution.
I am assigning you for this issue, however, please note that we accept high-quality implementations to our repository and will be glad to accept a contribution that meets our standards.
Feel free to reach out to the community for any questions! Good luck!