Master equation for adiabatic quantum computing

Presenting Author: Evgeny Mozgunov, University of Southern California

We present a spatially local Master equation for open system dynamics of a two-dimensional lattice of qubits in contact with a fast bath. The complete positivity of the evolution can be achieved via a previously known procedure of coarse-graining - time-averaging over a finite time. We show that the equation has a wider range of validity than the Lindblad equation with Davies generators. In particular, we do not require coupling to be exponentially weak in the system size. If the state remains a low bond dimension Matrix Product State throughout the evolution, the local equation can be simulated in time polynomial in system size. We also show how a widely used form \Delta^2/W of the tunneling rate through a potential barrier can be derived from this equation. Here \Delta is the splitting between states on the opposite sides of the barrier and W is the noise bandwidth.

Read this article online: https://arxiv.org/abs/1611.04188

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