Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.
Than et al. (Sun,) studied this question.