[PowerUp] Quantum Chemestry with restricted number of qubits

[JoseDCJesus]

Project Name: Quantum Chemestry with restricted number of qubits

Team Name: The Entangled Cats

Which challenges would you like to submit your project for? Quantum Chemistry Challenge Hybrid Quantum-Classical Computing Challenge Quantum computing today! QEC and Compilation Challenge

Power-Up plan: Our idea is to look at the BeH2 molecule, (which requires 12 qubits to evolve (considering a frozen core on Be, although this number can be brought even further down by freezing more orbitals (so far, we believe the minimum to be 8 qubits)) and obtain the ground state energy using VQE (possibly adapt-VQE) first on the IBM Power up. from the codding challenges (which gives access to 7 qubits) through circuit knitting and entanglement forging. This will allow us to compare these 2 new techniques. Then we want to compare the result with the evolution on a QPU with more than 12 qubits, and see if these 2 techniques have a meaningful impact on the calculated ground state energy, or no. To implement circuit knitting and entanglement forging we are using the Circuit Knitting Toolbox (https://qiskit-extensions.github.io/circuit-knitting-toolbox/index.html) and following these articles: https://arxiv.org/abs/2205.00016, https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.3.010309, https://arxiv.org/abs/2205.00933. If the results are positive this could pave the way for obtaining ground state energies of more complex molecules like CO2 in current NISQ.

As a last step, we plan to loop through the VQE using the different qubit mappers available on qiskit (currently using JordanWignerMapper) and see how the different maps affect the introduction of errors. Error mitigation techniques available on qiskit runtime will be used, and as a final touch, (if there is time) we intend to see if a simple VQE after a CNOT can be used to predict errors and correct them.

Project Link: (Here will be the link to your repository. Be sure to link to the corresponding commit as explained in the Readme) Example:

https://github.com/JoseDCJesus/QHackOpenHackathon/tree/f898a83df2668418f063da43747e4ac50f91c182 Remember not to modify this issue after the due date or it will not be evaluated

Access to power ups: If you have not yet done it, don't forget to fill in the form. In order to be eligible for power ups, the following fields must be completed with "Yes".

We allow Xanadu Quantum Technologies to share our email addresses with the Power-Up Sponsors for the purpose of facilitating the delivery of the Power-Ups.

Yes

(If applying for AWS’s credits) We have an AWS account

This is because the account ID is needed to give the power up. If you do not have a credit card, please contact AWS to find alternative access options.

Yes

(If applying for IBM’s dedicated slots) We confirm that We have filled in the form with the preferred slots.

Yes

(If applying for IBM’s dedicated slots) We have obtained an IBM ID

Yes