Digit quantum simulation of a fermion field in an expanding universe

TL;DR

This work tackles real-time quantum dynamics of fermions in curved spacetime by simulating a free fermion field in a 1+1D expanding universe with scale factor $g(t)=e^{ht}$. It employs digital quantum simulation using the Jordan–Wigner transformation and Trotter decomposition to evolve the lattice Hamiltonian derived from a 2D FLRW metric, enabling measurements of the fermion number density, density correlations, polarization, and chiral condensate. Key findings include momentum redshift–driven spreading of the fermion density, conformal invariance in the massless case eliminating expansion effects, and complex interplays between expansion and observables (e.g., polarization growth and oscillations of chiral condensation in the massive case). The results establish a framework for simulating QFT dynamics in curved spacetime on quantum hardware, identify practical hardware challenges (notably fidelity requirements for deeper circuits), and point toward future work incorporating interactions, gauge fields, and higher dimensions with error-correction strategies. These insights advance the feasibility of quantum simulations of early-universe phenomena and quantum gravity effects on near-term devices.

Abstract

Quantum simulation is a rapidly evolving tool with great potential for research at the frontiers of physics, and is particularly suited to be used in computationally intensive lattice simulations, such as problems with non-equilibrium. In this work, a basic scenario, namely free fermions in an expanding universe, is considered and quantum simulations are used to perform the evolution and study the phenomena involved. Using digital quantum simulations with the Jordan-Wigner transformation and Trotter expansion, the evolutions of fermion number density, correlation functions, polarization, and chiral condensation are analyzed. A spread out phenomenon can be observed in the simulation, which is a consequence of momentum redshift. This work also demonstrates the simplicity and convenience of using quantum simulations when studying time-evolution problems.

Figures (14)

• Figure 1: Results of $c(t=a/2)$ (left panel) and $c(t=a)$ (right panel) by using exact diagonalization for different $\Delta t$ as well as the linear extrapolations. It can be found that, the linear extrapolation is able to obtain the results at $\Delta t\to 0$.
• Figure 2: $c(t)$ as functions of $t$ for different $\Delta t$ compared with $c(t)$ obtained by using linear extrapolation.
• Figure 3: Starting from initial state $|1\rangle$, fermion number distribution changes with time evolution. The upper panels correspond to $m=0$, and the lower panels correspond to $am=1$, respectively. The left panels correspond to $ah=0.1$, and the right panels correspond to $h=0$, respectively.
• Figure 4: Same as Fig. \ref{['fig:fermionnumberstate1']} but for initial state $|254\rangle$.
• Figure 5: $\Delta n(x,t)$ as functions of time evolution, for the initial state $|1\rangle$. The left panel corresponds to $m=0$, and the right corresponds to $am=1$, respectively.