Machine-Learning-Enhanced Optimization of Noise-Resilient Variational Quantum Eigensolvers

TL;DR

This work addresses the fragility of variational quantum eigensolvers (VQEs) to noise on NISQ devices by introducing EMICoRe, a Gaussian-process–based Bayesian optimization framework tailored to the VQE objective. A physics-informed kernel, $k^{\mathrm{VQE}}$, encodes the known functional form of the VQE landscape, allowing the Gaussian process to sample functions consistent with the underlying physics, while the acquisition function EMICoRe selects measurements that most effectively reduce uncertainty within regions of high confidence. The NFT-with-EMICoRe algorithm integrates and extends the NFT approach by enabling learnable shifts and re-use of past data, achieving faster convergence and higher fidelity under hardware noise, particularly when combined with error mitigation techniques like TREX and ZNE. The numerical experiments on a 5-qubit Ising Hamiltonian at criticality demonstrate that EMICoRe outperforms NFT in energy minimization and fidelity in noisy simulations, suggesting a practical pathway toward more reliable VQE deployments on real quantum hardware and potential applications in lattice field theory.

Abstract

Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications, including lattice field theory. However, the inherent noise of Noisy Intermediate-Scale Quantum (NISQ) devices poses a significant challenge for running VQEs as these algorithms are particularly susceptible to noise, e.g., measurement shot noise and hardware noise. In a recent work, it was proposed to enhance the classical optimization of VQEs with Gaussian Processes (GPs) and Bayesian Optimization, as these machine-learning techniques are well-suited for handling noisy data. In these proceedings, we provide additional insights into this new algorithm and present further numerical experiments. In particular, we examine the impact of hardware noise and error mitigation on the algorithm's performance. We validate the algorithm using classical simulations of quantum hardware, including hardware noise benchmarks, which have not been considered in previous works. Our numerical experiments demonstrate that GP-enhanced algorithms can outperform state-of-the-art baselines, laying the foundation for future research on deploying these techniques to real quantum hardware and lattice field theory setups.

Figures (3)

• Figure 1: Illustration of the VQE workflow. For more details, see the text.
• Figure 2: Visualization of the EMICoRe algorithm. We refer to the main text for more details.
• Figure 3: Energy (left) and fidelity (right) for NFT (green) and EMICoRe (red). We show results for the critical Ising Hamiltonian using $Q = 5$ qubits and $L = 3$ layers, for an Efficient SU(2) quantum circuit, and $N_{\textrm{shots}} = 1024$ measurement shots. The top row displays runs with simulated hardware noise and no error mitigation, while the second and third rows present results with TREX and ZNE error mitigation schemes, respectively. The median (solid line) and the $25^\mathrm{th}$ and $75^\mathrm{th}$ percentiles (colored regions surrounding the median) are obtained with $50$ independent seeded runs for experiments in \ref{['fig:5-3-ising-noise']} and with $10$ runs for \ref{['fig:5-3-ising-noise-trex', 'fig:app_5-3-ising-noise-zne']}. A density of the trial distribution at the end of the optimization is shown right next to each plot.