The search of an unstructured database amounts to finding one element having a certain property out of $N$ elements. The classical search with an oracle checking one element at a time requires on average $N/2$ steps. The Grover algorithm for the quantum search, and its unitary Hamiltonian evolution analogue, accomplish the search asymptotically optimally in $\mathcal{O} (\sqrt{N})$ time steps. We reformulate the search problem as a dissipative Markov process acting on an $N$-level system weakly coupled to a thermal bath. Assuming that the energy levels of the system represent the database elements, we show that, with a proper choice of the spectrum and physically admissible, long-range transition rates between the energy levels, the system relaxes to the ground state, corresponding to the sought element, in time $\mathcal{O} (\ln N)$.

翻译：无结构数据库的搜索相当于找到一个元素,该元素的属性来自$N元的元素。古典搜索,先用甲骨文检查一个元素,一次平均需要2美元。量子搜索的格罗佛算法及其单一的汉密尔顿进化模拟,以$\mathcal{O}(\sqrt{N})美元的时间步骤以非同步的最佳方式完成了搜索。我们重新将搜索问题描述为一个分离的马尔科夫进程,在美元水平的系统上,微弱地配合热浴。假设该系统的能量水平代表了数据库元素,我们表明,如果对频谱进行适当选择,并且可以实际接受,系统在能量水平之间的长距离转换速度,在时间($mathcal{O} (\ n) 时,系统将放松到地面状态,与所寻求的元素相对应,相当于时间($mathcal{O} (=N) 美元。