Dynamics of disordered quantum systems with two- and three-dimensional tensor networks

Large-scale quantum annealing dynamics of Ising spin glasses were recently implemented on D-Wave's Advantage2 system on a range of lattices. After extensive comparison with existing numerical methods, these experiments were claimed to be beyond the reach of classical computation. Here, we simulated these spin-glass models with lattice-specific tensor networks, using belief propagation (BP) to keep up with the entanglement generated during the time evolution and then extracting expectation values with more sophisticated variants of BP. We found that state-of-the-art accuracies could be achieved with modest computational resources. Moreover, our results are scalable in both two and three dimensions, which we leveraged to verify universal Kibble-Zurek physics on systems involving hundreds of qubits.