Error mitigation method by the University of Tokyo results in higher accuracy in quantum computing calculations of Hückel molecular orbitals

A research group led by graduate student Ryuhei Yoshida, Associate Professor Erik Lötstedt, and Professor Kaoru Yamanouchi of School of Science, the University of Tokyo, has used the quantum computer ibm_kawasaki to calculate the energies of molecular orbitals of basic molecules such as ethylene, 1, 3-butadiene, and benzene using the Hückel molecular orbital method, a simple molecular orbital method. The results showed that orbital energies can be obtained with high accuracy and precision if error mitigation is done to discard physically meaningless states generated by errors in quantum calculations.

The research group has advanced the Applied Quantum Chemistry by Qubits (AQUABIT) project with support from the University of Tokyo's Quantum Initiative and DIC and has worked to develop a methodology for computing molecular systems using a quantum computer and to improve the accuracy of calculations by suppressing errors in quantum computer results.

An ideal quantum computer can instantly perform calculations on a scale that has been impossible to date. However, current quantum computers make errors, meaning the calculation results must be corrected. In a concerete system, the goal is to use a quantum computer to perform calculations and demonstrate how useful they can be.

In their research, the University of Tokyo group has demonstrated that orbital energies can be determined with high accuracy and precision by incorporating the simplest error mitigation (a method of correcting errors in quantum gate operations), which is to discard physically meaningless states generated by errors in quantum calculations. The method is so basic that it provides a guideline for the instantaneous determination of electronic states of large pi-conjugated systems such as fullerenes, graphene, and carbon nanotubes by quantum computers.

"As the probability of error decreases with technological advances in quantum computer hardware, we can expect to see an increasing number of targets for which quantum computer calculations will be meaningful," says Professor Yamanouchi. "The next step is to take full advantage of those technological advances and work on the quantum computing of large systems such as fullerenes and carbon nanotubes, for example."

■ Hückel method: A molecular orbital method proposed by German physical chemist Erich Hückel in 1930. It describes the molecular orbitals of pi-conjugated molecules and their energies. Molecular orbitals are superpositions of the atomic orbitals of carbon atoms, and only one p-orbital per carbon atom is considered. The values of the Coulomb integral and resonance integral are assumed to be the same in the molecule as α and β, respectively.

Journal Information
Publication: The Journal of Chemical Physics
Title: Quantum computing of Hückel molecular orbitals of π-electron systems
DOI: 10.1063/5.0086489