Imaginary-time evolution algorithm on quantum computers and its perspective on quantum chemical calculations
Currently, quantum chemical calculations using quantum computers are attracting a great deal of attention. We have been developing algorithms for quantum chemical calculations using quantum computers. In particular, we have recently focused on the imaginary-time evolution method. Note that algorithms using quantum computers must be expressed in terms of unitary operations and observations for each qubit. Therefore, it was a nontrivial problem how to perform the imaginary-time evolution operator, which is a non-unitary operation, on a quantum computer. We have developed a method to implement the imaginary-time evolution algorithm in a form using auxiliary bits and proposed a method of first-quantized eigensolver for quantum chemistry for ground states based on the imaginary-time evolution method [1]. Furthermore, we have been working on developing algorithms to reduce errors when performing calculations on quantum computers [2]. In this presentation, we will discuss the fundamentals of quantum computers, the implementation of the imaginary-time evolution algorithm, the computational cost of implementing the imaginary-time evolution algorithm for materials calculations, and the error mitigation algorithms we have been developing.
[1] T. Kosugi, Y. Nishiya, and Y. Matsushita, arXiv: 2111.12471 (2021). To be published in Physical Review Research.[2] Y. Hama and H. Nishi, arXiv: 2205.13907 (2022).