Quantum Computing Simulation of a Phase Change in a Cavity Quantum Electrodynamics Hamiltonian

We investigate the application of quantum computers to the investigation of effects in cavity quantum electrodynamics (“cavity QED”), which are relevant for areas like materials properties, multiphoton effects such as superradiance or systems with strong field-matter coupling. To study these systems, we introduce a boson-to-qubit mapping to facilitate a multi-photon, multi-atom case study, based on the inverse Holstein-Primakoff transformation. In the multi-photon regime, boson operators are expressed via higher-spin operators which are subsequently mapped on a circuit using Pauli operators. We use a Newton series expansion to enable rigorous treatment of the square root operator. With this encoding, we perform simulations of a phase transition in a pair of coupled cavities that permit photon hopping using 6 qubits. We map the spin and boson systems to separate qubit registers and use first-order Trotterization to time-propagate the wavefunction. The order parameter, the observable for the phase transition, is calculated by measuring the number operator and its square. We find that the simulation matches benchmark classical calculations and the phase transition is well resolved with a relatively small amount of shots, indicating that our encoding properly represents the physics of the system, and the simulation can be performed with a modest amount of quantum resources on hardware.