  The imaginary-time evolution of quantum states is integral to various fields,
ranging from natural sciences to classical optimization or machine learning.
Since simulating quantum imaginary-time evolution generally requires storing an
exponentially large wave function, quantum computers are emerging as a
promising platform for this task. However, variational approaches, suitable for
near-term quantum computers, struggle with a prohibitive number of measurements
and impractical runtimes for relevant system sizes. Here, we suggest a
stochastic approach to variational quantum imaginary-time evolution, which
allows a significant reduction in runtimes. Our approach allows trading off
invested resources and accuracy, which makes it also suitable for ground state
preparation, where simulating the exact dynamics is not required. We
demonstrate the efficiency of our algorithm in simulations and show a hardware
experiment performing the imaginary-time evolution of the transverse field
Ising model on 27 qubits.
