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Toward perturbation theory methods on a quantum computer.
Junxu Li1,2, Barbara A Jones3, Sabre Kais1
1Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA.
Science Advances
|May 12, 2023
Summary
Quantum computing offers a superior alternative to classical methods for perturbation theory. This new quantum circuit accurately estimates energy corrections for complex systems, outperforming classical approaches.
Area of Science:
- Quantum Computing
- Computational Physics
- Theoretical Chemistry
Background:
- Perturbation theory is a fundamental method for approximating solutions to complex problems.
- Classical computation faces limitations in solving large-scale quantum systems.
- Recent advances in quantum computing present new avenues for computational methods.
Purpose of the Study:
- To develop and demonstrate a general quantum circuit for estimating energy and eigenstate corrections.
- To showcase the superiority of the quantum approach over classical methods for second-order energy corrections.
- To apply the quantum circuit to the two-site extended Hubbard model.
Main Methods:
- Implementation of a general quantum circuit for perturbation theory.
- Numerical simulations using qiskit.
- Execution and results analysis on IBM's quantum hardware.
- Application to the two-site extended Hubbard model.
Main Results:
- The developed quantum circuit significantly outperforms classical methods for second-order energy corrections.
- Accurate estimation of energy and eigenstate corrections was achieved.
- Demonstrated feasibility and performance on real quantum hardware.
Conclusions:
- Quantum computing provides a powerful and efficient tool for perturbation theory.
- The proposed quantum circuit offers a generalizable approach for studying complex Hamiltonian systems.
- This method eliminates the need for training or optimization processes to obtain perturbative terms.
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