Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers

Abstract

The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi-Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi-Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi-Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Finally, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

Figures (10)

• Figure 1: Quantum circuit representation of the single Trotter step used in the first-order Trotterization for $L=4$ fermion sites ($N=8$ qubits).
• Figure 2: Quantum circuit of the single Trotter step in the second-order Trotterization for $L=4$ fermion sites ($N=8$ qubits).
• Figure 3: Quantum circuit of the second-order Trotterization with two Trotter steps $r=2$ for $L=4$ fermion sites ($N=8$ qubits).
• Figure 4: Quantum circuit of the optimized second-order Trotterization with three Trotter steps $r=3$.
• Figure 5: The total circuit depth with respect to the number of Trotter step for the quantum circuit of the first-order, second-order, and optimized second-order Trotterization describing the time evolution driven by the Fermi-Hubbard model.