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Suitable computational conditions of adiabatic state preparation discovered for quantum chemical calculations

A research group including Dr. Kenji Sugisaki, Professor Kazunobu Sato, and Professor Emeritus Takeji Takui from the Graduate School of Science, Osaka Metropolitan University, has investigated the specific computational conditions for Adiabatic State Preparation (ASP) executable on a quantum computer; ASP is considered one of the leading methods for efficiently taking into account electron correlation effects in the wave function of molecules.

ASP is a method to obtain the exact wave function by simulating the time evolution of the wave function under a time-dependent Hamiltonian. The Hamiltonian is an operator that defines all the relevant physical energies, such as the motion and interactions between electrons and nuclei that make up a molecule. ASP gradually changes a Hamiltonian whose eigenfunction is easy-to-prepare, to a true Hamiltonian during the quantum simulation of time evolution. However, the specific conditions for performing these calculations have not been investigated to a great extent, rendering their use impractical.

Numerical simulation results of ASP in a structure in which two Be-H bonds of the BeH2 molecule are simultaneously elongated.

The left figure shows the length of time to vary the Hamiltonian with ASP and the right figure shows the overlap squared value with the full-configuration integration calculation of the wave function (as the overlap squared approaches 1, the better the approximation accuracy of the wave function).

To make the method more versatile, the research group has performed ASP numerical simulations under various conditions. As a result, the following four points have become clear:

1. When starting from the Hartree–Fock wave function, controlling the time variation of the Hamiltonian as sinusoidal functions gives the best performance.
2. The amount of time to change the Hamiltonian should be inversely proportional to the HOMO–LUMO energy gap of a molecule under consideration.
3. For electronic structures with open shell low-spin electronic configurations, a broken-symmetry wave function can be used to generate an accurate wave function with fewer steps.
4. When using a broken-symmetry wave function, the length of time to change the Hamiltonian should be constant regardless of the molecular structure.

The research team has also proposed a simple method for determining whether the Hartree–Fock or broken-symmetry wave function should be used as an initial wave function. The team has demonstrated that these four points are relevant to the computational conditions for using ASP, making broader use practical for the first time.

“ASP is considered a powerful method for facilitating the preparation of correlated wave functions on a quantum computer, but the specific computational conditions that should be used have been unclear until now. With this study, I believe ASP has eventually become practical. In the future, I expect this approach will be used to design new materials based on theoretical calculations using quantum computers,” said Dr. Kenji Sugisaki.

Funding

This work was supported by JST PRESTO “Quantum Software” project (Grant No. JPMJPR1914), Japan, and KAKENHI Scientific Re-search C (Grant No. 18K03465 and 21K03407) from JSPS, Japan, and partially supported by AOARD Scientific Project on “Molecular Spins for Quantum Technologies” (Grant FA2386-17-1-4040, 4041), USA.

Paper Information

Title: Adiabatic state preparation of correlated wave functions with nonlinear scheduling functions and broken-symmetry wave functions
Journal: Communications Chemistry
DOI: 10.1038/s42004-022-00701-8
Author: Kenji Sugisaki, Kazuo Toyota, Kazunobu Sato, Daisuke Shiomi, and Takeji Takui
Communications Chemistry (Springer Nature Website)

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Contact

Graduate School of Science
Dr. Kenji SUGISAKI
E-mail sugisaki[at]omu.ac.jp  *Please change [at] to @.
Professor Takeji TAKUI
E-mail takui[at]omu.ac.jp  *Please change [at] to @.