Simulating the Dicke Model on Qubit-Based and hybrid Qubit-Boson-Based Quantum Computers

Research Question and Approach

The Dicke model is a cornerstone of quantum optics, describing how an ensemble of two-level atoms interacts with a single-mode bosonic field. While it is theoretically well-understood, simulating it on quantum computers is challenging due to the infinite-dimensional nature of the bosonic Hilbert space. This paper introduces a variational framework to simulate the finite-size Dicke model by using an inverse Holstein-Primakoff transformation to map the bosonic cavity mode onto a finite number of qubits. The authors construct symmetry-preserving variational ansätze that exploit the parity, time-reversal, and exchange symmetries of the Hamiltonian, which helps stabilize the optimization process and reduces the search space for the Variational Quantum Eigensolver (VQE).

The researchers demonstrate that their "spin-Dicke" model—a qubit-based representation of the Dicke Hamiltonian—successfully reproduces the characteristic critical behavior of the original model as the number of qubits increases. By utilizing a problem-inspired ansatz that respects the system's inherent symmetries, the authors achieve accurate ground- and excited-state calculations across various coupling strengths. The framework was validated using statevector simulations and tested on a trapped-ion quantum processor. Additionally, the paper introduces a hybrid qubit-bosonic ansatz that treats the cavity as a bosonic degree of freedom, which effectively reduces the total number of qubits and circuit depth required for implementation.

This work provides a scalable, symmetry-aware pathway for simulating collective light-matter interactions on near-term quantum devices. By reformulating complex spin-boson models into qubit-compatible formats, the authors enable the study of inhomogeneous systems—where atomic frequencies and couplings vary—which are often intractable for classical supercomputers. This approach bridges the gap between theoretical quantum optics and practical implementation on noisy intermediate-scale quantum (NISQ) hardware.