Variational ansatz-based quantum simulation of imaginary time evolution

• Published in: npj quantum information Vol. 5; no. 1; pp. 1 - 6
• Main Authors: McArdle, Sam, Jones, Tyson, Endo, Suguru, Li, Ying, Benjamin, Simon C., Yuan, Xiao
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 06-09-2019; Nature Publishing Group
• Subjects: 639/766/483/3926; 639/766/483/481; Algorithms; Classical and Quantum Gravitation; Computers; Evolution; Learning algorithms; Lithium; Physics; Physics and Astronomy; Quantum Computing; Quantum Field Theories; Quantum Information Technology; Quantum Physics; Relativity Theory; Spintronics; String Theory
• ISSN: 2056-6387; 2056-6387
• DOI: 10.1038/s41534-019-0187-2

Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a variational algorithm for simulating imaginary time evolution on a hybrid quantum computer. We use this algorithm to find the ground-state energy of many-particle systems; specifically molecular hydrogen and lithium hydride, finding the ground state with high probability. Our method can also be applied to general optimisation problems and quantum machine learning. As our algorithm is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, it can be implemented with current quantum computers.