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

摘要

We propose a method to interpolate dynamics of von Neumann and classicalmaster equations with an arbitrary coupling strength to study thermal effectsin quantum dynamics. A formulation of mixing the two dynamics is given by notdirectly introducing a coupling term but an intervention of the two dynamicsthrough modification of their solutions continuously to couple the systemsindirectly. This method keeps the quantum system in a pure state even thermaleffects are introduced. Consequently, not only density matrix but also statevector representation can be obtained. In a two-level system, we demonstratethat the dynamics can be rewritten as a standard differential equationrepresentation, which results in quantum dynamics with relaxation. Thedifferential equations are equivalent to optical Bloch equations at the weakcoupling and asymptotic limits, and that implies the dynamics naturallyintroduces thermal effects in quantum dynamics. Numerical calculations offerromagnetic and frustrated systems support the speculation. Finally, we applythis method to study thermal effects in quantum annealing. In a spin glassmodel, nontrivial performance improvement was observed with a specific range ofannealing duration. This finding may help to optimize the annealing duration inthe real annealing machine.