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Numerical Investigation of the Quantum Inverse Algorithm on Small Molecules.
Mauro Cainelli1, Reo Baba1, Yuki Kurashige1,2,3
1Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan.
Journal of Chemical Theory and Computation
|September 11, 2024
Summary
The quantum inverse (Q-Inv) algorithm offers lower energy results than inverse iteration (I-Iter) for quantum chemistry calculations. Combining integration methods improves convergence and reduces computational cost, especially for challenging systems.
Area of Science:
- Quantum Chemistry
- Computational Physics
- Theoretical Chemistry
Background:
- Accurate calculation of molecular energies is crucial in quantum chemistry.
- The quantum inverse (Q-Inv) algorithm offers an alternative to traditional inverse iteration methods.
- Numerical integration accuracy significantly impacts the performance of quantum algorithms.
Purpose of the Study:
- To evaluate the accuracy of the Q-Inv algorithm across various molecular systems.
- To investigate the impact of integration parameters and iteration power (k) on Q-Inv accuracy.
- To compare Q-Inv with inverse iteration (I-Iter) and exact inverse methods.
Main Methods:
- The Q-Inv algorithm, replacing matrix multiplication with Fourier transforms.
- Comparison of trapezoidal integration with Gaussian-quadrature rules.
- Evaluation of energy values as expectation values of the Hamiltonian.
- Benchmarking against I-Iter and lower-upper decomposition methods.
Main Results:
- Q-Inv yields lower energies than I-Iter up to a specific iteration power (k).
- Numerical integration errors increase with k, dependent on the integration interval.
- Combined Gaussian-quadrature and trapezoidal integration enhance convergence and reduce operations.
- A hybrid Q-Inv and I-Iter approach is proposed for systems like H4 to reduce errors.
Conclusions:
- The Q-Inv algorithm's accuracy is sensitive to integration parameters and iteration power.
- Optimized integration strategies are key to achieving reliable Q-Inv results.
- Hybrid methods can overcome limitations of individual algorithms for complex systems.
- A recommended procedure for treating unknown systems using Q-Inv is outlined.
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