Researchers have developed a field theory describing the kinetics of defects emerging during quantum annealing computations, particularly when the system passes through or approaches a first-order phase transition. Unlike second-order transitions, first-order transitions involve a stage where the system becomes trapped in a metastable state. The decay of this metastable state leads to abundant excitations above the ground state, resulting in errors in quantum computation.

The theory predicts several power laws for the error generation rate as a function of quantum annealing parameters. A key aspect is the prediction of sharp changes in the exponents of these power laws for continuous parameter variations. Experimental observation of this behavior would be a clear signature of the presence of first-order critical points in the annealing process. Identifying and potentially avoiding these critical points is crucial for improving the reliability and performance of quantum annealers.

To validate their approach, the authors used the driven Lipkin-Meshkov-Glick model (LMGm), which serves as a minimal model of interacting Ising spins. This model is capable of demonstrating the predicted behavior of first-order phase transitions and the associated error generation. The work provides a theoretical foundation for better understanding the limitations of current quantum annealers and future strategies for error mitigation.