Error Mitigation of Hamiltonian Simulations from an Analog-Based Compiler (SimuQ)

Quantum computing has emerged as a revolutionary paradigm with the potential to solve computationally intractable problems. However, the practical realization of quantum al-gorithms faces significant challenges due to noise and errors inherent in quantum systems. Hamiltonian simulations serve as a cornerstone in quantum computing, providing insights into quantum dynamics and enabling the study of quantum algorithms. This paper studies error mitigation in analog-based Hamiltonian simulations as they have native support for generating Hamiltonians as opposed to digital-based simulations, which results in shorter pulse schedules to simulate the Hamiltonians. We further aim to enhance the accuracy and reliability of these simulations through error mitigation techniques. This research explores several error mitigation techniques tailored for analog-based Hamiltonian simulations. Among them, Zero-Noise Extrapolation (ZNE) mitigates errors by extrapolating simulation results to the ideal noise-free scenario. Building upon ZNE, Folding-Free ZNE (FFZNE) introduces novel use of the infinite error point to address the challenges posed by folding techniques. Additionally, Reliability-Based ZNE (RBZNE) leverages a mix of both techniques, utilizing the folding method and the infinite error point. Through empirical studies and rigorous analysis, this paper evaluates the efficacy and limitations of these error mitigation techniques in analog-based Hamiltonian simulations on both noise simulator and real quantum hardware. The experimental results shed light on the comparative performance of ZNE, FFZNE, and RBZNE, understanding their strengths and weak-nesses in mitigating errors across different quantum systems and noise conditions. By providing the understanding of these techniques, this research contributes to the advancement of error mitigation strategies in quantum computing, paving the way for more reliable and accurate quantum simulations.