This research introduces practical Quantum Error Mitigation (QEM) techniques for Quantum Annealing (QA) systems, specifically using Zero-Noise Extrapolation (ZNE) methods. While quantum error correction remains the ultimate solution for quantum computing errors, QEM offers a more immediately applicable approach for today’s quantum systems.
The researchers developed two key ZNE implementations: zero-temperature extrapolation and zero-time extrapolation. The latter innovatively leverages the Kibble-Zurek mechanism, requiring only problem-Hamiltonian rescaling rather than more complex adjustments. These techniques allow estimation of error-free expectation values when noise impacts are relatively small.
Experimental validation focused on the quantum critical and post-critical dynamics of a transverse-field Ising spin chain. The team examined statistics with both weak and strong post-critical dynamics, successfully demonstrating mitigation of thermal noise and non-thermal errors through both extrapolation methods.
The extrapolated results showed strong alignment with exact solutions and time-dependent density matrix renormalization group simulations for closed system Schrödinger evolution across various control parameters. Investigations covered both kink density and kink correlations, revealing that kink density follows the Kibble-Zurek mechanism with errors primarily from thermal noise, while kink correlations proved more sensitive to post-critical dynamics and non-thermal errors.
This work represents an important advance in practical QEM for quantum annealing. Unlike previous quantum-annealing correction techniques, these methods enhance expectation value accuracy without requiring additional qubits. The research builds upon earlier experimental attempts to extract noise-free evolution information through extrapolation, where QA performance was examined as a function of temperature for problems with minimal spectral gaps.
While other error-mitigation proposals for QA exist, they remain largely theoretical with limited practical application to existing quantum-annealing processors. This research bridges theory and implementation, providing experimentally validated techniques that can improve the performance of current quantum annealing systems as they explore complex quantum states and phase transitions.
Raymond, J., Amin, M.H., King, A.D. et al. Quantum error mitigation in quantum annealing.npj Quantum Inf 11, 38 (2025). doi:10.1038/s41534-025-00977-3