  Quantum Monte Carlo simulations are powerful and versatile tools for the
quantum many-body problem. In addition to the usual calculations of energies
and eigenstate observables, quantum Monte Carlo simulations can in principle be
used to build fast and accurate many-body emulators using eigenvector
continuation or design time-dependent Hamiltonians for adiabatic quantum
computing. These new applications require something that is missing from the
published literature, an efficient quantum Monte Carlo scheme for computing the
inner product of ground state eigenvectors corresponding to different
Hamiltonians. In this work, we introduce an algorithm called the floating block
method, which solves the problem by performing Euclidean time evolution with
two different Hamiltonians and interleaving the corresponding time blocks. We
use the floating block method and nuclear lattice simulations to build
eigenvector continuation emulators for energies of $^4$He, $^8$Be, $^{12}$C,
and $^{16}$O nuclei over a range of local and non-local interaction couplings.
From the emulator data, we identify the quantum phase transition line from a
Bose gas of alpha particles to a nuclear liquid.
