QSciTech-QuantumBC Virtual Workshop 2023: Quantum Chemistry with Gate-Based Quantum Computing Using IBM Quantum

My implementation of the Variational Quantum Eigensolver (VQE) applied to the $H_2$ molecule can be found in this repository. This was created during the QSciTech-QuantumBC Virtual Workshop 2023.

In detail, the following is covered:

VQE experiments on both the ideal QASM simulator and IBM Quantum Computers for different bond distances in the H2 molecule. IBM-Q implementation trough Qiskit runtime so that error mitigation techniques can be easily activated (see resilience_level and documentation https://qiskit.org/documentation/partners/qiskit_ibm_runtime/how_to/error-mitigation.html).

Additionally, for comparison, the exact solution for the ground state energy is computed through diagonalization of the Hamiltonian.

Results:

Three main results (see plot below)

1. Simulated VQE matches exact solutions ●
2. (Uncorrected) IBMQ overestimates ▼
3. Error mitigation improves IBMQ results by mitigating the overestimation x

Poster:

See my team's poster on the project here: Final poster.pdf

Special thanks to my team members for the good collaboration!

Disclaimer:

This implementation served the purpose to understand and learn the concepts involved in this Quantum Chemistry application for (Gate-based) IBM Quantum Computers. IBQ already provides complete implementations for VQE including molecule mappings to qubits in Qiskit. Please refer to https://qiskit.org/textbook/ch-applications/vqe-molecules.html and for details using the Qiskit Runtime https://qiskit.org/documentation/partners/qiskit_ibm_runtime/tutorials/vqe_with_estimator.html

Implementation by Jonas Jäger [email protected]

File overview:

Description of the files (beyond the original template files as listed below):

• dissociation_vals.csv: Contains experimental results
• experiments.ipynb: Performs VQE experiments on both the ideal QASM simulator and IBM Quantum Computers for different bond distances in the H2 molecule and computes exact results.
• plot.pdf: Plot showing the experimental results compared to the exact dissociation curve (PDF)
• plot.png: Plot showing the experimental results compared to the exact dissociation curve (PNG)
• plots.ipynb: Plots the experimental results

Acknowledgements:

Me and my team sincerely thank CMC, QsiTech, QuantumBC for this informative workshop, and IBM for providing the quantum hardware.

Original template description

Notebook template by Maxime Dion [email protected]

Incomplete version of the suggested solution to find the ground state of a molecule using quantum computing.

Description of the files :

• hamiltonian.py : This files defines the FermionicHamiltonian class and subclasses. You should be able to partially complete it after the lecture on second quantization. The 'to_linear_combinaison_pauli_string' methods can be completed after the lecture on mapping.
• pauli_string.py : Defines PauliString and LinearCombinaisonPauliString class. You should be able to complete it after the lecture on mapping. The 'to_matrix' method is optional.
• mapping.py : Defines the JordanWigner mapping. You should be able to complete it after the lecture on mapping.
• estimator.py : Defines the abstract class Estimator and the BasicEstimator class. You should be able to complete it after the lecture on VQE.
• solver.py : Defines VQESolver and ExactSolver. You should be able to complete it after the lecture on VQE. The ExactSolver is optionnal.

Other files :

• Integrals_sto-3g_H2_d_0.7350_no_spin.npz : Contains the one body and two body integrals (no spin) for a H2 molecule with d=0.735. The two body is given in the physicist order.
• activity_mapping_.ipynb and activity_vqe_.ipynb : Tutorial Jupyter notebooks to help you code the concepts seen in the respective activities.