  Quantum simulation of quantum field theory is a flagship application of
quantum computers that promises to deliver capabilities beyond classical
computing. The realization of quantum advantage will require methods to
accurately predict error scaling as a function of the resolution and parameters
of the model that can be implemented efficiently on quantum hardware. In this
paper, we address the representation of lattice bosonic fields in a discretized
field amplitude basis, develop methods to predict error scaling, and present
efficient qubit implementation strategies. A low-energy subspace of the bosonic
Hilbert space, defined by a boson occupation cutoff, can be represented with
exponentially good accuracy by a low-energy subspace of a finite size Hilbert
space. The finite representation construction and the associated errors are
directly related to the accuracy of the Nyquist-Shannon sampling and the Finite
Fourier transforms of the boson number states in the field and the
conjugate-field bases. We analyze the relation between the boson mass, the
discretization parameters used for wavefunction sampling and the finite
representation size. Numerical simulations of small size $\Phi^4$ problems
demonstrate that the boson mass optimizing the sampling of the ground state
wavefunction is a good approximation to the optimal boson mass yielding the
minimum low-energy subspace size. However, we find that accurate sampling of
general wavefunctions does not necessarily result in accurate representation.
We develop methods for validating and adjusting the discretization parameters
to achieve more accurate simulations.
