Decoherence in adiabatic quantum computation

We have studied the decoherence properties of adiabatic quantum computation (AQC) in the presence of in general non-Markovian, e.g., low-frequency, noise. The developed description of the incoherent Landau-Zener transitions shows that the global AQC maintains its properties even for decoherence larger than the minimum gap at the anticrossing of the two lowest-energy levels. The more efficient local AQC, however, does not improve scaling of the computation time with the number of qubits $n$ as in the decoherence-free case. The scaling improvement requires phase coherence throughout the computation, limiting the computation time and the problem size $n$.

Figure 1

(Color online) Broadening of the energy levels of a closed system (a) due to coupling to an environment made of (b) a single two-state system or (c) infinitely many degrees of freedom with a continuous energy spectrum. In general, the coupling to an environment splits a single anticrossing into $M^2$ anticrossings, where $M$ is the number of environment energy eigenstates. For the environment with a continuous spectrum, the anticrossing turns into a continuous transition region of width $W$.

Figure 2

The occupation probability $p_G$ of the ground state as a function of the dimensionless evolution time $\gamma t_f$ for different temperatures $T$ in the case of the Gaussian tunneling rates (5). The inset shows the dependence of $p_G$ on $T/W$ for $\gamma t_f=1$, 1.5, 2, 3, and 5 from lower to upper curves, respectively.