  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.

Quantum Physics