Digital Qubit-Boson Circuits and their Advantages for Quantum Simulation of Lattice Gauge Theories

Quantum simulation of lattice gauge theories (LGTs) has been a subject of intense interest in high energy and condensed matter physics because computing dynamics and ground states is classically hard. In addition to fermionic sectors, which can be efficiently encoded with qubits, many lattice gauge theories contain bosonic excitations, which have an infinite Hilbert space leading to extremely high gate counts when encoded on qubits, thus threatening the ability of quantum simulation to address theories which contain bosons. Extensive progress has recently been made in the fabrication and control of microwave cavity resonators, which naturally host a bosonic Hilbert space and are coupled to transmon qubits, and may therefore be able to more efficiently encode the bosonic sectors of LGTs, though these systems are still in development. Despite the excitement linked to this mixed qubit-boson platform, it is unclear whether the currently available hardware would outperform all-qubit hardware for the simulation of lattice gauge theories in terms of gate counts, circuit fidelities, and total number of shots. This is hard to verify because: the relative complexity of simulating gauge-theoretic operators with qubit-boson hardware vs qubit-only hardware is unknown, due to the lack of compiler we must design the fermion-boson gates in the mixed qubit-boson hardware, the effects of noise for deep, multi-qubit/qumode circuits required for high fidelity simulations have yet to be quantified. Considerable previous literature exists on novel approaches for simulating LGTs but these methods are challenging to extend to higher dimensions. In this paper, we provide an example of an experimental architecture for a 1+1D mixed boson-fermion system which efficiently performs ground state preparation for both the Z2 gauge theory coupled to bosonic matter and the Schwinger model and show, using 'Bosonic Qiskit' which we previously developed, that it would dramatically outperform all-qubit systems, featuring much lower gate counts by three orders of magnitude, far higher circuit fidelities, and fewer total shots to successfully capture the essential physics of these theories.