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

As recently reported by the newspaper Chemistry Physical Physical Chemical, researchers at the Graduate School of Science at Osaka University have developed a quantum algorithm that can understand the electronic states of atomic or molecular systems by directly calculating the energy difference in their relevant states. Implemented as a different Bayesian estimate of phase, the algorithm breaks with convention by not focusing on the difference in total energies calculated from the pre- and post-phase evolution, but by following the evolution of the energy difference itself.

“Almost all chemistry problems deal with the difference in energy, not the total energy of the molecule itself,” explains research manager and specially appointed lecturer Kenji Sugisaki, “moreover, molecules with Heavy atoms that appear in the lower part of the periodic table have large total energies, but the size of the energy difference discussed in chemistry, such as electronic excitation states and ionization energies, does not depend very much on the size of the molecule. This idea led Sugisaki and his team to implement a quantum algorithm that directly calculates energy differences instead of total energies, creating a future where evolutionary or practical quantum computers allow us to conduct real chemical research and materials development.

Currently, quantum computers are able to perform the full configuration interaction (full CI) calculations that allow optimal molecular energies with a quantum algorithm called quantum phase estimation (QPE), noting that the calculation of CI complete for large molecular systems is insoluble with any supercomputer. 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 that ‘an atom or a molecule – time – changes its phase evolutionarily according to its total energy. In the classical QPE, the quantum superposition state (| 0⟩ | Ψ⟩ + | 1⟩ | Ψ⟩) ⁄ √2 is prepared, and the introduction of a controlled temporal evolution operator makes | Ψ⟩ evolve in time only when the first qubit designates the state | 1⟩. Thus, the state | 1⟩ creates a quantum phase of the post-evolution in time while the | 0⟩ state that of the pre-evolution. The phase difference between the pre- and post-evolutions gives the total energy of the system.

Researchers at Osaka City University generalize conventional QPE to the direct calculation of the total energy difference between two relevant quantum states. In the new quantum algorithm called Bayesian phase difference estimation (BPDE), the superposition of the two wave functions, (| 0⟩ | Ψ₀ + | 1⟩ | Ψ₁ ⟩) ⁄ √2, where | Ψ₀ and | Ψ₁ ⟩ Denotes the wave function relating to each state, respectively, is prepared, and the phase difference between | Ψ₀ and | Ψ₁ ⟩ After time, the evolution of the superposition directly gives the total energy difference between the two wave functions involved. “We emphasize that the algorithm follows the evolution of the energy difference over time, which is less prone to noise than the individual calculation of the total energy of an atom or a molecule. Thus, l The algorithm responds to the need for chemistry problems that require precise energy precision. ” says Research Director and Emeritus Professor Takeji Takui.

Previously, this research group developed a quantum algorithm that directly calculates the energy difference between electronic states (spin states) with different spin quantum numbers (K. Sugisaki, K. Toyota, K. Sato, D. Shiomi , T. Takui, Chem. Sci. 2021, 12, 2121–2132.). This algorithm, however, requires more qubits than conventional QPE and cannot be applied to calculating the energy difference between electronic states with equal spin quantum numbers, which is important for spectral attribution of spectra. UV-visible absorption. The BPDE algorithm developed in the study overcomes these problems, making it a very versatile quantum algorithm.

Provided by Osaka City University