Quantum error mitigation has been extensively explored to increase the accuracy of the quantum circuits in noisy-intermediate-scale-quantum (NISQ) computation, where quantum error correction requiring additional quantum resources is not adopted. Among various error-mitigation schemes, probabilistic error cancellation (PEC) has been proposed as a general and systematic protocol that can be applied to numerous hardware platforms and quantum algorithms. However, PEC has only been tested in two-qubit systems and a superconducting multi-qubit system by learning a sparse error model. Here, we benchmark PEC using up to four trapped-ion qubits. For the benchmark, we simulate the dynamics of interacting fermions with or without spins by applying multiple Trotter steps. By tomographically reconstructing the error model and incorporating other mitigation methods such as positive probability and symmetry constraints, we are able to increase the fidelity of simulation and faithfully observe the dynamics of the Fermi–Hubbard model, including the different behavior of charge and spin of fermions. Our demonstrations can be an essential step for further extending systematic error-mitigation schemes toward practical quantum advantages.

量子误差缓解已被广泛探索，以提高噪声中尺度量子（NISQ）计算中量子电路的精度，其中不采用需要额外量子资源的量子误差校正。在各种错误缓解方案中，概率错误消除（PEC）已被提出作为一种通用且系统的协议，可应用于多种硬件平台和量子算法。然而，PEC 仅通过学习稀疏误差模型在两个量子位系统和超导多量子位系统中进行了测试。在这里，我们使用最多四个捕获离子量子位对 PEC 进行基准测试。对于基准测试，我们通过应用多个 Trotter 步骤来模拟有或没有自旋的费米子相互作用的动力学。通过层析重建误差模型并结合其他缓解方法（例如正概率和对称约束），我们能够提高模拟的保真度并忠实地观察费米-哈伯德模型的动力学，包括费米子的电荷和自旋的不同行为。我们的演示可以成为进一步扩展系统误差缓解方案以实现实际量子优势的重要一步。