Quantum Chemistry on Quantum Computers

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Quantum computing and quantum information processing technology have attracted attention in recently emerging fields. Among many important and fundamental issues in nowadays science, solving Schroedinger Equation (SE) of atoms and molecules is one of the ultimate goals in chemistry, physics and their related fields. SE is "First Principle" of non-relativistic quantum mechanics, whose solutions termed wave functions can afford any information of electrons within atoms and molecules, predicting their physicochemical properties and chemical reactions.

Researchers from Osaka City University (OCU) in Japan, Dr. K. Sugisaki, Profs. K. Sato and T. Takui and coworkers have found a novel quantum algorithm enabling us to determine whether quantum chemical calculations performed on quantum computers give correct wave functions as exact solutions of SE in a desired manner. These issues are intractable with any currently available supercomputers. Such a quantum algorithm contributes to the acceleration of implementing practical quantum computers.

Nowadays chemistry and physics have sought to predict complex chemical reactions by invoking Full-CI approaches since 1929, but never been successful until now. Now Full-CI calculations are potentially capable of predicting chemical reactions, and a new Full-CI approach suitable for predicting the physicochemical properties has already been implemented on quantum computers. Now, the possible methodological implementation of "observables on quantum computers" such as calculating the spin quantum numbers of arbitrary wave functions, which is a crucial issue in quantum chemistry, has been established by the OCU research group.

They said, "As Dirac claimed in 1929 when quantum mechanics was established, the exact application of mathematical theories to solve SE leads to equations too complicated to be soluble1. In fact, the number of variables to be determined in the Full-CI method grows exponentially against the system size, and it easily runs into astronomical figures such as exponential explosion. For example, the dimension of the Full-CI calculation for benzene molecule C6H6, in which only 42 electrons are involved, amounts to 1044, which are impossible to be dealt with by any supercomputers.

What is worse, molecular systems during the dissociation process are characterized by extremely complex electronic structures (reconfiguration nature), and relevant numerical calculations are impossible on any supercomputers. Besides these intrinsic difficulties, there has been a difficult issue in the emerging fields such as determining physical quantities relevant to quantum chemistry on quantum computers."