Mitsubishi Chemical Group Corporation (Headquarters: Chiyoda-ku, Tokyo, President: Manabu Chikumoto), Keio University (Located: Minato-ku, Tokyo, President: Kohei Itoh), Softbank Corporation (Headquarters: Minato-ku, Tokyo, President: Junichi Miyakawa), and JSR Corporation (Headquarters: Minato-ku, Tokyo, President: Tetsuro Hori) have developed a method for energy gap calculation of large systems using quantum computers. This work is the result of collaborative efforts within the IBM Quantum Network Hub, a part of the Keio University Quantum Computing Center. The resulting manuscript has been published in the Proceedings of the National Academy of Sciences (PNAS) and can be accessed at the following URL: Tensor-based quantum phase difference estimation for large-scale demonstration | PNAS.