Error-Mitigated Quantum Simulation of Interacting Fermions with Trapped Ions

TL;DR

This paper demonstrates the application of probabilistic error cancellation to improve the fidelity of quantum simulations of interacting fermions on trapped-ion qubits, advancing error mitigation in NISQ devices.

Contribution

It extends PEC benchmarking from small systems to four trapped-ion qubits, enabling more accurate simulation of complex fermionic dynamics.

Findings

Increased simulation fidelity with PEC and additional mitigation methods.

Successful observation of Fermi-Hubbard model dynamics, including charge and spin behavior.

Benchmarking of PEC in a trapped-ion platform with up to four qubits.

Abstract

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.