  The capacity for solving eigenstates with a quantum computer is key for
ultimately simulating physical systems. Here we propose inverse iteration
quantum eigensolvers, which exploit the power of quantum computing for the
classical inverse power iteration method. A key ingredient is constructing an
inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution.
We first consider a continuous-variable quantum mode (qumode) for realizing
such a linear combination as an integral, with weights being encoded into a
qumode resource state. We demonstrate the quantum algorithm with numerical
simulations under finite squeezing for various physical systems, including
molecules and quantum many-body models. We also discuss a hybrid
quantum-classical algorithm that directly sums up Hamiltonian evolution with
different durations for comparison. It is revealed that continuous-variable
resources are valuable for reducing the coherent evolution time of Hamiltonians
in quantum algorithms.
