Variational quantum simulation of imaginary time evolution
Imaginary time evolution is a powerful tool for studying quantum systems. While it is simple to simulate with a classical computer, the time and memory requirements scale exponentially with the system size. Conversely, quantum computers can efficiently simulate quantum systems, but not non-unitary imaginary time evolution. We propose a hybrid, variational algorithm for simulating imaginary time evolution on a 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.
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