# New Bayesian quantum algorithm calculates the energy difference of an atom and molecule

A newly developed quantum algorithm can understand the electronic states of atomic or molecular systems. It does so by calculating the energy difference in their relevant states.

Developed by researchers from the Graduate School of Science at Osaka City University, the algorithm is a Bayesian phase different estimation (BPDE). It breaks from convention by following the evolution of the energy difference itself.

Existing quantum computers can perform full configuration interaction (full-CI) calculations because of a quantum algorithm called quantum phase estimation (QPE). QPE relies on the fact that a wave function, |Ψ⟩ which denotes the mathematical description of the quantum state of a microscopic system – in this case, the mathematical solution of the Schrödinger equation for the microscopic system such as an atom or molecule – time-evolutionally changes its phase depending on its total energy.

Scientists, in this study, generalize the conventional QPE to the direct calculation of the difference in the total energy between two relevant quantum states.

In the new algorithm, the superposition of the two wave functions, (|0⟩|Ψ0 ⟩ + |1⟩|Ψ1 ⟩) ⁄ √2, where |Ψ0 ⟩ and |Ψ1 ⟩ denote the wave function relevant to each state, respectively, is prepared. The difference in the phase between |Ψ0 ⟩ and |Ψ1 ⟩ after the time evolution of the superposition directly gives the difference in the total energy between the two wave functions involved.

Research supervisor and Professor Emeritus Takeji Takui said,* “We emphasize that the algorithm follows the evolution of the energy difference over time, which is less prone to noise than individually calculating the total energy of an atom or molecule. Thus, the algorithm suites the need for chemistry problems which require precise accuracy in energy.”*

The BPDE algorithm is highly versatile that solved issues in the previously developed quantum algorithm that requires more qubits than the conventional QPE and cannot be applied to the energy difference calculation. This is important for the spectral assignment of UV-visible absorption spectra.

##### Journal Reference:

- Kenji Sugisaki et al. Bayesian phase difference estimation: a general quantum algorithm for directly calculating energy gaps. DOI: 10.1039/D1CP03156B