Digital quantum simulations of the limit shape transition in massive integrable quantum field theories

We propose a polynomial-time quantum algorithm to simulate the quench dynamics of massive integrable quantum field theories on a digital quantum computer, starting from a multi-particle limit-shape initial state. This process is expected to exhibit a dynamical phase transition of the Gross–Witten–Wadia universality class, manifested by a Loschmidt echo with distinct behaviors in short- and long-time regimes. Meanwhile, obtaining the Loschmidt echo classically in general requires summing over an exponential number of permutations of particle labels with S-matrix weights. We therefore argue that simulating this process on quantum hardware may offer potential quantum advantage over classical simulation. Our results provide a concrete testbed for quantum simulation of exotic dynamical processes in interacting quantum many-body systems, which also open a new avenue for showcasing advantages of quantum simulators.