[Paper Review] Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Frank Arute, Kunal Arya+97 more|arXiv (Cornell University)|Oct 15, 2020

Quantum and electron transport phenomenaPhysics and Astronomy72 references94 citations

TL;DR

The authors simulate the 1D Fermi-Hubbard model on 16 superconducting qubits, demonstrating spin-charge separation in highly excited dynamics and introducing Floquet calibration and error-mitigation techniques to extend circuit depth.

ABSTRACT

Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.

Motivation & Objective

• Demonstrate time evolution of the 1D Fermi-Hubbard model on a digital quantum processor.
• Observe separation between charge and spin spreading velocities beyond low-energy theories.
• Develop and apply fast gate calibration (Floquet calibration) to mitigate drifts in entangling gates.
• Implement error-mitigation strategies to extend usable circuit depths in a noisy quantum device.

Proposed method

• Map the 1D Fermi-Hubbard Hamiltonian to qubits via Jordan-Wigner transformation for each spin state.
• Use Trotterization with a 5-stage gate sequence to implement one time step of evolution.
• Employ a native two-qubit gate family K(θ) combined with CPHASE-like interactions to realize hopping and interaction terms.
• Apply Floquet calibration to rapidly characterize and correct entangling-gate parameters.
• Use qubit-assignment averaging and postselection on excitation numbers to mitigate SPAM and decoherence errors.
• Rescale damped experimental observables against numerical predictions to recover faithful dynamics.

Experimental results

Research questions

• RQ1 Can the dynamics of spin and charge densities in the 1D Fermi-Hubbard model be observed to separate in a highly excited regime on a digital quantum processor?
• RQ2 How do Floquet calibration and error-mitigation techniques extend coherent simulation depth for strongly correlated models?
• RQ3 What is the impact of interaction strength on the relative spreading speeds of spin and charge in this setup?

Key findings

• Spin and charge densities exhibit separated spreading velocities in the strongly interacting regime (u = U/J ≥ 1).
• Charge density spreads faster than spin density and reaches boundaries earlier.
• Floquet calibration enables rapid, precise gate parameter characterization robust to SPAM errors, extending feasible circuit depths by about an order of magnitude.
• Qubit-assignment averaging plus postselection and rescaling yield experimentally observed dynamics that align with numerical predictions despite >600 two-qubit gates.
• Differences between noninteracting and interacting cases are consistent with expectations from the model dynamics and gate-induced parasitics.