Written by AZoQuantumJan 3 2019

**In newly emerging fields, quantum information processing and quantum computing technologies have attracted a great deal of attention.**

Among the various fundamental and significant problems in today’s science, cracking Schroedinger Equation, or SE, of molecules and atoms is one of the crucial objectives in physics, chemistry, and their associated fields.

SE is “First Principle” of non-relativistic quantum mechanics, the solutions of which known as wave functions have the ability to provide any kind of information on electrons within molecules and atoms, forecasting their chemical reactions and physicochemical properties.

At Osaka City University (OCU) in Japan, a research team, which included Dr K. Sugisaki, Professors T. Takui and K. Sato, and coworkers, has discovered a new quantum algorithm that enables performing full configuration interaction, or Full-CI, calculations appropriate for “chemical reactions” without combinatorial or exponential explosion. The precise numerical solutions of SE, which are inflexible issues associated with any kind of supercomputers, is provided by Full-CI. A quantum algorithm of this kind plays a role in expediting the implementation of practical quantum computers. Since 1929, physics and chemistry have always sought to estimate intricate chemical reactions by invoking Full-CI methods but have never been successful to date. At present, Full-CI calculations have the ability to predict complex chemical reactions, and for the first time, the novel Full-CI method appropriate for the prediction is being implemented on quantum computers.

The results of the study will be published in *ACS (American Chemical Society) Central Science* on January 2^{nd}, 2019.

According to the team, “*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 soluble. 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 C*_{6}H_{6}, 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 (multiconfigurational nature), and relevant numerical calculations are impossible on any supercomputers.”

The OCU research team believes that quantum computers can date back to a Feynman’s proposal in 1982, which indicates that it is possible to simulate quantum mechanics through a computer made of quantum mechanical elements, which obey the laws of quantum mechanics. After more than two decades later, Prof. Aspuru-Guzik, Harvard University (Toronto University since 2018), and colleagues suggested a quantum algorithm that has the ability to determine the energies of molecules and atoms polynomially, not exponentially, against the number of the systems’ variables, thus making an innovation in the field of quantum chemistry on quantum computers.

If Aspuru’s quantum algorithm is used on the Full-CI calculations on quantum computers, then excellent approximate wave functions close to the precise wave functions of SE being studied will be needed, or else, substandard wave functions require more numbers of steps of repeated calculations in order to achieve the precise ones, thus obstructing the benefits of quantum computing. However, this issue turns out to be quite serious when analyzing chemical reactions, which have several multiconfigurational nature because electrons do not take part in chemical bonding at the time of bond dissociation. The OCU team has resolved this problem, which happens to be one among the most intractable problems in quantum chemistry and quantum science, and advanced the implementation of a novel quantum algorithm creating specific wave functions called configuration state functions, or CSFs, in polynomial computing time in the years 2016 and 2018.

However, the formerly suggested algorithms for quantum computing are still challenging to efficiently solve SE for entire chemical reaction pathways, which inexorably involve the formation and dissociation of a number of chemical bonds and consequently create so many electrons that do not take part in chemical bonds. As a result, the quantum algorithms become too complicated to apply, termed “Quantum Dilemma.”

A “diradical character, yi(0 ~ 1)” has been introduced by the OCU team to calculate and define the nature of open shell electronic structures. The researchers exploited the diradical characters to build multiconfigurational wave functions needed for chemical reactions, performing the Full-CI calculations along the entire reaction pathways on quantum computers. This novel procedure eliminates time-intensive advanced post-Hartree-Fock calculations and, for the first time, prevents the exponential explosion of the calculation and solving “Quantum Dilemma.”

According to the OCU team, “*This is the first example of a practical quantum algorithm, which makes quantum chemical calculations for predicting chemical reaction pathways realizable on quantum computers equipped with a sizable number of qubits. The implementation empowers practical applications of quantum chemical calculations on quantum computers in many important fields of chemistry and materials science*.”