Thermally Assisted Adiabatic Quantum Computation

We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is super-Ohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that performance better than classical is possible with a super-Ohmic environment, with no a priori knowledge of the energy spectrum.

Figure 1

Ground and first excited states of a system with one anticrossing at $\lambda =0.5$. The three regions are identified in such a way that $g>T$ for regions I and III, and $g<T$ for region II.

Figure 2

Probability of success for AGS with 12 (blue or gray), 16 (red or light gray), and 20 (green or dark gray) qubits, and a super-Ohmic environment with $s=0.5$ at $T/E=0.1$. The solid and dotted curves are for longitudinal (${\overline{\eta }}^x=0$, ${\overline{\eta }}^z=0.1$) and transverse (${\overline{\eta }}^x=0.1$, ${\overline{\eta }}^z=0$) couplings to the environment, respectively. The solid black line represents a closed system (${\overline{\eta }}^x={\overline{\eta }}^z=0$), which with the normalized $x$ axis is independent of $n$.