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We propose a method to interpolate dynamics of von Neumann and classicalmaster equations with an arbitrary mixing parameter to investigate the thermaleffects in quantum dynamics. The two dynamics are mixed by intervening tocontinuously modify their solutions, thus coupling them indirectly instead ofdirectly introducing a coupling term. This maintains the quantum system in apure state even after the introduction of thermal effects and obtains not onlya density matrix but also a state vector representation. Further, wedemonstrate that the dynamics of a two-level system can be rewritten as a setof standard differential equations, resulting in quantum dynamics that includesthermal relaxation. These equations are equivalent to the optical Blochequations at the weak coupling and asymptotic limits, implying that thedynamics cause thermal effects naturally. Numerical simulations offerromagnetic and frustrated systems support this idea. Finally, we use thismethod to study thermal effects in quantum annealing, revealing nontrivialperformance improvements for a spin glass model over a certain range ofannealing time. This result may enable us to optimize the annealing time ofreal annealing machines.

Dynamics of open quantum systems by interpolation of von Neumann and classical master equations, and its application to quantum annealing