Quantum simulation of cosmic inflation

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 Hamilton-Kabat-Lifschytz-Lowe-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.

Figure 1

The encoding process from the past light cone. Here, we use a two-dimensional plot to illustrate past light cones for different $\tau \mathrm{s}$ at a fixed $\mathbf{x}$. Those light cones are intersected with the time slice ${\tau }_0$. We use a one-dimensional real line to represent the direction of $\mathbf{x}$, but in the real world, we have three spatial dimensions.

Figure 2

The AdS-Rindler bulk reconstruction. Here the bulk operators could be reconstructed from the boundary using the HKLL reconstruction formula. This is the standard example mentioned in, for instance, [66].

Figure 3

The one-loop diagram at the fixed time ${\tau }_0$.