This research presents a Digital-Analog Quantum Computing (DAQC) approach for simulating the Hubbard-Holstein model, which describes strongly correlated fermion-boson interactions in solid-state physics. This model is fundamental to understanding phenomena like polaron formation and plays a vital role in determining transport properties in various materials including biomolecules, cuprates, fullerides, and manganites.
The authors propose a hardware-software co-design architecture using superconducting circuits arranged in a linear chain of qubits connected by resonators. This configuration naturally enables the simulation of electron-electron interactions, electron-phonon interactions, and fermion tunneling. The DAQC paradigm combines analog blocks (leveraging the natural evolution of the system) with digital steps to create an efficient simulation algorithm.
When compared to purely digital approaches, this method demonstrates significant advantages in terms of circuit depth reduction and simulation fidelity. For a test case involving a half-filled two-site Hubbard-Holstein model, the researchers achieved time-dependent state fidelities exceeding 0.98, confirming the approach’s viability for studying dynamical behaviors in solid-state systems.
The work addresses the fundamental challenge of simulating strongly correlated fermionic systems, which are typically intractable using classical computing methods beyond a few particles. Traditional approximation techniques like mean-field theories, quantum Monte Carlo, and tensor network methods each have limitations, particularly in capturing correlation effects.
The proposed superconducting circuit implementation offers advantages over other quantum simulation platforms such as trapped ions or cold atoms. It benefits from the possibility of adding multiple waveguide cavities or LC oscillators, making it ideal for compact simulations of systems with multiple bosonic modes.
This research has significant implications for exploring phase diagrams and polaron formation, with potential applications in materials science, chemistry, and high-energy physics. It represents an important step toward utilizing quantum computing to solve complex problems that remain beyond the reach of classical computing approaches.
Reference: Kumar, S., Hegade, N.N., Visuri, AM. et al. Digital-analog quantum computing of fermion-boson models in superconducting circuits. npj Quantum Inf 11, 43 (2025). doi:10.1038/s41534-025-01001-4
