Digital-analog quantum computing of fermion-boson models in superconducting circuits

TL;DR

This paper introduces a digital-analog quantum algorithm for simulating fermion-boson models, specifically the Hubbard-Holstein model, using superconducting circuits, achieving high fidelity and reduced circuit depth for studying complex condensed matter systems.

Contribution

It presents a novel digital-analog quantum computing approach tailored for fermion-boson models in superconducting circuits, improving efficiency over purely digital methods.

Findings

Achieved time-dependent state fidelities > 0.98 in simulations.

Reduced circuit depth compared to digital-only approaches.

Demonstrated suitability for studying dynamical behavior in solid-state systems.

Abstract

High-fidelity quantum simulations demand hardware-software co-design architectures, which are crucial for adapting to complex problems such as strongly correlated dynamics in condensed matter. By leveraging co-design strategies, we can enhance the performance of state-of-the-art quantum devices in the noisy intermediate quantum (NISQ) and early error-correction regimes. In this direction, we propose a digital-analog quantum algorithm for simulating the Hubbard-Holstein model, describing strongly-correlated fermion-boson interactions, in a suitable architecture with superconducting circuits. It comprises a linear chain of qubits connected by resonators, emulating electron-electron (e-e) and electron-phonon (e-p) interactions, as well as fermion tunneling. Our approach is adequate for digital-analog quantum computing (DAQC) of fermion-boson models, including those described by the Hubbard-Holstein model. We show the reduction in the circuit depth of the DAQC algorithm, a sequence of digital steps and analog blocks, outperforming the purely digital approach. We exemplify the quantum simulation of a half-filled two-site Hubbard-Holstein model. In this example, we obtain time-dependent state fidelities larger than 0.98, showing that our proposal is suitable for studying the dynamical behavior of solid-state systems. Our proposal opens the door to computing complex systems for chemistry, materials, and high-energy physics.