Advantages of Digital Qubit-Boson Hardware for Quantum Simulation

Finding a straightforward, scalable and universal framework for quantum simulation of strongly correlated fermions and bosons is important from material science to high-energy physics. Here, we develop hybrid qubit-oscillator operations for microwave cavities coupled to transmon qubits required for implementing dynamics of bosonic matter, fermionic matter, and Abelian gauge fields in (2+1)D. We then expand the method to ground state preparation and propose measurement of various long-range correlation functions required for the study of phase transitions. We implement numerical proof of principle experiments for a (1+1)D Z2 Bose Hubbard (BH) gauge theory and the U(1) Schwinger model. We include the main sources of hardware noise, which we mitigate through post-selection based on Gauss' law. This new approach motivates us to uncover the phase diagram of the Z2 BH model, relevant to the Higgs sector. We discover a new phase of matter which exhibits strong density fluctuations which we dub the `clump' phase. Finally, we perform a complexity analysis and find that for one Trotter step of these example models, qubit systems require higher gate counts than our proposal by three orders of magnitude. Our correspondingly higher circuit fidelities may help us to successfully capture the essential physics of these theories in the near-term.