Quantum Bayesian Optimization for the Automatic Tuning of Lorenz-96 as a Surrogate Climate Model

TL;DR

This paper introduces a quantum-inspired heuristic for automatically tuning the Lorenz-96 climate model, demonstrating quantum kernel superiority in simulations and discussing pathways for real quantum hardware implementation.

Contribution

It proposes replacing classical Gaussian process emulators with quantum kernels and benchmarks their performance, advancing quantum methods in climate model tuning.

Findings

Quantum kernels outperform classical RBF kernel in simulations.

The method is NISQ-friendly with low qubit requirements.

Quantum-inspired approach improves tuning accuracy.

Abstract

In this work, we propose a hybrid quantum-inspired heuristic for automatically tuning the Lorenz-96 model -- a simple proxy to describe atmospheric dynamics, yet exhibiting chaotic behavior. Building on the history matching framework by Lguensat et al. (2023), we fully automate the tuning process with a new convergence criterion and propose replacing classical Gaussian process emulators with quantum counterparts. We benchmark three quantum kernel architectures, distinguished by their quantum feature map circuits. A dimensionality argument implies, in principle, an increased expressivity of the quantum kernels over their classical competitors. For each kernel type, we perform an extensive hyperparameter optimization of our tuning algorithm. We confirm the validity of a quantum-inspired approach based on statevector simulation by numerically demonstrating the superiority of two studied quantum kernels over the canonical classical RBF kernel. Finally, we discuss the pathway towards real quantum hardware, mainly driven by a transition to shot-based simulations and evaluating quantum kernels via randomized measurements, which can mitigate the effect of gate errors. The very low qubit requirements and moderate circuit depths, together with a minimal number of trainable circuit parameters, make our method particularly NISQ-friendly.