Observation of quantum-field-theory dynamics on a spin-phonon quantum computer: Theory

Quantum simulation is a promising approach to study out-of-equilibrium dynamics of quantum gauge field theories, particularly in regimes where classical methods become intractable. Mapping bosonic (gauge) degrees of freedom onto qubits requires truncating their infinite dimensional Hilbert space, leading to errors that grow with system energy and simulation time, and resulting in a large qubit and gate overhead in fully digital schemes. An alternative method is to augment the qubit-based quantum computer with controllable bosonic degrees of freedom, enabling hybrid architectures that naturally implement qubit, bosonic and qubit-bosonic gates. In this work, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a fermion-boson quantum field theory, on a trapped-ion platform where qubits are encoded in the ions’ internal levels and bosons in their motional modes. The fermion- and boson-occupation state probabilities were measured and found to be in good agreement with classical simulations, even for high phonon occupations. This hybrid approach 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. In this talk, we present the theoretical foundations of this work, with a subsequent talk covering the experimental implementation and results.