Quantum computing simulation of a mixed spin-boson Hamiltonian and its performance for a cavity quantum electrodynamics problem

In this paper, we aim to broaden the spectrum of possible applications of quantum computers and use their capabilities to investigate effects in cavity quantum electrodynamics (cavity QED). Interesting application examples are material properties, multiphoton effects such as superradiance, systems with strong field-matter coupling, and others. For QED applications, experimental studies are challenging, and classical simulations are often expensive. Therefore, exploring the capabilities of quantum computers is of interest. Below we present a methodology for simulating a phase transition in a pair of coupled cavities that permit photon hopping. We map the spin and boson systems to separate parts of the register and use first-order Trotterization to time-propagate the wave function. The order parameter, the observable for the phase transition, is calculated by measuring the number operator and its square. We introduce a boson-to-qubit mapping to facilitate a multiphoton, multiatom case study. Our mapping scheme is based on the inverse Holstein-Primakoff transformation. In the multiphoton 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. We reproduce the results of classical simulations of a phase transition with a noiseless six-qubit simulation. We find that the simulation can be performed with a modest amount of quantum resources. Finally, we perform simulations on noisy emulators and find that mitigation techniques are essential to distinguish signal from noise.