Quantum field theory dynamics on a spin–phonon quantum computer

Abstract

Simulating the non-equilibrium dynamics of quantum field theories in nature is generally intractable with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields using quantum computers typically requires a boson-to-qubit encoding that can be resource-intensive. Furthermore, these encodings necessarily involve a truncation of the infinite-dimensional Hilbert space, introducing errors that grow with energy and time. Here we adopt an alternative approach that combines a qubit-based quantum computer with an active bosonic register that offers qubit, bosonic and mixed qubit–boson quantum gates. We use a hybrid analogue–digital trapped-ion quantum computer in which qubits are encoded in the internal states of the ions as well as the bosons in the ions’ motional states. Specifically, we simulate the non-equilibrium dynamics of a (1 + 1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions. These dynamics populate high-bosonic-field excitations starting from an empty state, and the experimental results effectively capture such high-occupation states. By removing the need for a large qubit overhead and avoiding truncation errors, our simulation approaches the regime in which classical methods become challenging. Many physical systems involve bosons, which are resource-intensive to simulate with a qubit-based quantum computer. Now a hybrid approach that combines qubits and bosons has been used to simulate a quantum field theory of fermions and bosons.