Measurement of the incoherent decay rate of quantum states in quantum annealing with a D-Wave machine

Abstract Quantum annealing has been demonstrated with superconducting qubits. Such a quantum annealer has been used to solve combinational optimization problems. Moreover, it serves as a quantum simulator for investigating the properties of the quantum many-body systems. However, the coherence properties of actual devices provided by D-Wave Quantum Inc. have not been explored sufficiently. Here, we measure the energy relaxation of the excited state in quantum annealing with the D-Wave device. Specifically, we investigate the incoherent decay rate of the first excited states of a fully connected Ising model with a transverse field. We find that the decay rate of the excited states of the model is orders of magnitude smaller than that of the excited state of a single qubit, and we qualitatively explain this phenomenon by using theoretical methods. Since our numerical simulations show that the first excited state during QA for the model is entangled, our experimental results indicate that the long-lived entangled state can be generated during QA with the D-Wave machine.