Experimental Quantum Simulation of the Yukawa Model on a Hybrid Spin-Phonon Quantum Computer

The Yukawa model is a scalar field theory which captures fundamental elements of the strong force by modeling the interaction between nucleons and pions. While the fermionic nucleons can be efficiently encoded into qubits, simulating the bosonic pions on a traditional quantum computer necessitates truncation of the bosonic field, leading to truncation errors mitigated only at considerable cost in qubit number and/or gate depth. In this work we demonstrate an alternative way to encode the model's bosonic field into a controlled degree of freedom which is natively bosonic, the joint harmonic motion of trapped ions. Using a hybrid spin-phonon quantum computer consisting of just three ions, we quantum simulated quench dynamics of the 1+1D Yukawa model with two and four lattice sites, experimentally resolving the generation of at least ten pionic excitations across multiple modes. I will briefly discuss the challenges and opportunities for future work along two lines: the refinement of experimental control over larger numbers of phonon modes and the application of this type of simulator to lattice gauge theories.