  In this paper, we generalize Jordan-Lee-Preskill, an algorithm for simulating
flat-space quantum field theories, to 3+1 dimensional inflationary spacetime.
The generalized algorithm contains the encoding treatment, the initial state
preparation, the inflation process, and the quantum measurement of cosmological
observables at late time. The algorithm is helpful for obtaining predictions of
cosmic non-Gaussianities, serving as useful benchmark problems for quantum
devices, and checking assumptions made about interacting vacuum in the
inflationary perturbation theory.
  Components of our work also include a detailed discussion about the lattice
regularization of the cosmic perturbation theory, a detailed discussion about
the in-in formalism, a discussion about encoding using the HKLL-type formula
that might apply for both dS and AdS spacetimes, a discussion about bounding
curvature perturbations, a description of the three-party Trotter simulation
algorithm for time-dependent Hamiltonians, a ground state projection algorithm
for simulating gapless theories, a discussion about the quantum-extended
Church-Turing Thesis, and a discussion about simulating cosmic reheating in
quantum devices.
