Adiabatic Quantum Computation in Open Systems

We analyze the performance of adiabatic quantum computation (AQC) subject to decoherence. To this end, we introduce an inherently open-systems approach, based on a recent generalization of the adiabatic approximation. In contrast to closed systems, we show that a system may initially be in an adiabatic regime, but then undergo a transition to a regime where adiabaticity breaks down. As a consequence, the success of AQC depends sensitively on the competition between various pertinent rates, giving rise to optimality criteria.

Figure 1

$T_{\alpha }^c$ as a function of $T$ for the Jordan blocks $J_2$, $J_3$, and $J_4$. The inset of (a) shows that $J_2$ has non-negligible couplings for $T\sim {10}^3$ (in units such that $\omega =1$).