Quantum annealing aims at finding optimal solutions to complex optimization problems using a suitable quantum many body Hamiltonian encoding the solution in its ground state. To find the solution one typically evolves the ground state of a soluble, simple initial Hamiltonian adiabatically to the ground state of the designated final Hamiltonian. Here we explore whether and when a full quantum representation of the dynamics leads to higher probability to end up in the desired ground when compared to a classical mean field approximation. As simple but nontrivial example we target the ground state of interacting bosons trapped in a tight binding lattice with small local defect by turning on long range interactions. Already two atoms in four sites interacting via two cavity modes prove complex enough to exhibit significant differences between the full quantum model and a mean field approximation for the cavity fields mediating the interactions. We find a large parameter region of highly successful quantum annealing, where the semi-classical approach largely fails. Here we see strong evidence for the importance of entanglement to end close to the optimal solution. The quantum model also reduces the minimal time for a high target occupation probability. Surprisingly, in contrast to naive expectations that enlarging the Hilbert space is beneficial, different numerical cut-offs of the Hilbert space reveal an improved performance for lower cut-offs, i.e. an nonphysical reduced Hilbert space, for short simulation times. Hence a less faithful representation of the full quantum dynamics sometimes creates a higher numerical success probability in even shorter time. However, a sufficiently high cut-off proves relevant to obtain near perfect fidelity for long simulations times in a single run. Overall our results exhibit a clear improvement to find the optimal solution based on a quantum model versus simulations based on a classical field approximation.

中文翻译：

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揭示量子退火与半经典退火相比成功概率更高的起源

量子退火旨在使用合适的量子多体哈密顿量找到复杂优化问题的最佳解决方案，该哈密顿量将解决方案编码为基态。为了找到解决方案，通常将可溶性简单初始哈密顿量的基态绝热演化为指定的最终哈密顿量的基态。在这里，我们探索与经典平均场近似相比，动力学的完整量子表示是否以及何时导致更高的概率最终到达所需的地面。作为一个简单但重要的例子，我们通过开启远程相互作用，将相互作用玻色子的基态锁定在具有小局部缺陷的紧束缚晶格中。四个位点中的两个原子通过两个腔模式相互作用已经证明足够复杂，以显示完整量子模型与调解相互作用的腔场的平均场近似之间的显着差异。我们发现了一个非常成功的量子退火的大参数区域，其中半经典方法在很大程度上失败了。在这里，我们看到了纠缠对接近最优解的重要性的有力证据。量子模型还减少了高目标占用概率的最短时间。令人惊讶的是，与扩大希尔伯特空间有益的天真期望相反，希尔伯特空间的不同数值截断揭示了较低截断的改进性能，即非物理减少的希尔伯特空间，用于较短的模拟时间。因此，完整量子动力学的不太忠实的表示有时会在更短的时间内产生更高的数值成功概率。然而，事实证明，足够高的截止值对于在单次运行的长时间模拟中获得近乎完美的保真度是相关的。总体而言，与基于经典场近似的模拟相比，我们的结果显示出基于量子模型找到最佳解决方案的明显改进。