Quemix and Honda Research Institute Develop New Technology to Exponentially Accelerate 'Density Functional Calculations', the Core Technology of Material DX, on Quantum Computers

Quemix Inc., a group company of TerraSky Co., Ltd. that conducts R&D on quantum computer algorithms and software, and Honda Research Institute Co., Ltd., the R&D division of Honda Motor Co., Ltd., have successfully developed the world's first quantum algorithm that exponentially improves the calculation speed of 'Density Functional Theory (DFT)', the core technology of Material DX, as a result of joint research.

DFT calculations, currently a fundamental technique in material computation, are considered an extremely important core technology that impacts all areas of material development. By developing this quantum algorithm for accelerating DFT calculations, we have unlocked the potential to execute DFT calculations on massive systems that were previously impossible with conventional computers. In the future, applying this algorithm to practical tasks is expected to accelerate the speed of new material development, an area Honda Research Institute focuses on.

[Background: 'DFT', the Core of Material DX, and Expectations for Quantum Computers]
In recent years, there has been an urgent need to shift from conventional experimental-driven material development based on 'experience and intuition' to 'Material Digital Transformation (Material DX)' utilizing computational science. The core technology of Material DX is Density Functional Theory (DFT), an electronic state calculation method. DFT is an indispensable tool in modern material design because it can predict the properties of substances at the atomic level.

Meanwhile, quantum computers are anticipated as the next-generation computational platform. Research is accelerating worldwide to realize 'speedup' and 'higher precision' in simulations that were difficult for conventional classical computers by leveraging quantum computers.

[Past Challenges: Focus on Precision and Absence of Speedup Algorithms]
Until now, most research on material simulation using quantum computers has focused on 'higher precision'. This is because quantum computers are adept at handling 'electron-electron interactions (electron repulsion)' precisely.

- Targets for high precision: Analysis of 'strongly correlated substances' where electron-electron interactions are very strong, or 'excited states' such as photo-reactions.

Challenges: However, many materials in high industrial demand, such as pharmaceuticals, semiconductors, and battery materials, are classified as 'weakly correlated substances'. For these material calculations, DFT calculation is sufficient, and higher speed or larger scale is more required than higher precision.

Furthermore, regarding the speedup of DFT calculations, which is the heart of Material DX, there have been no effective quantum algorithms until now. The reason is that it was technically extremely difficult to incorporate the non-linear calculation processes unique to DFT calculations into the linear computational system of quantum computers.

Specifically, the 'Gram-Schmidt orthogonalization method' included in the DFT calculation process is a non-linear operation, and has been a major challenge in implementation on quantum circuits. Also, when evaluating total energy, the formula itself is defined as a non-linear functional of electron density distribution, so sequential reading (sampling) of electron density distribution was indispensable in conventional methods. This large computational cost accompanying this 'reading' has also been a major bottleneck hindering practical application.

[This Achievement: Development of the World's First DFT Speedup Algorithm]
Quemix and Honda Research Institute have successfully developed the world's first new quantum algorithm that exponentially accelerates DFT calculations using quantum computers. This algorithm builds a new quantum algorithm that avoids the Gram-Schmidt orthogonalization method, and further constructs a method to calculate total DFT energy directly from the sampling results of the QPE (Quantum Phase Estimation) circuit without reading electron density. As a result, we have successfully constructed a fast DFT calculation scheme that requires no reading of electron density distribution for the first time in the world.

■ Results of Demonstration Experiments
We executed the developed algorithm on an emulator and confirmed the following points:

- Exponential speedup: Confirmed that as the calculation scale increases, the calculation time is exponentially shortened compared to conventional algorithms.
- Precision equivalent to conventional methods: Successfully obtained high-precision results comparable to conventional DFT in calculating interatomic distances and structural constants (parameters of crystal structures).
- Advanced physical property prediction: Demonstrated that it is possible to calculate 'electronic band structure', which determines the electrical properties of materials.