Quantum annealing, which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states. However, such excited-state quantum annealing is prone to errors due to dissipation. Here we propose excited-state quantum annealing started with the most stable state, i.e., vacuum states. This counterintuitive approach becomes possible by using effective energy eigenstates of driven quantum systems. To demonstrate this concept, we use a network of Kerr-nonlinear parametric oscillators, where we can start excited-state quantum annealing with the vacuum state of the network by appropriately setting initial detuning frequencies for the oscillators. By numerical simulations of four oscillators, we show that the present approach can solve some hard instances whose optimal solutions cannot be obtained by standard ground-state quantum annealing because of energy-gap closing. In this approach, a nonadiabatic transition at an energy-gap closing point is rather utilized. We also show that this approach is robust against errors due to dissipation, as expected, compared to quantum annealing started with physical excited (i.e., nonvacuum) states. These results open new possibilities for quantum computation and driven quantum systems.

量子退火对于组合优化特别有用，除基态外，还通过使用激发态而变得更强大。但是，这样的激发态量子退火容易因耗散而产生误差。在这里，我们提出以最稳定的状态（即真空状态）开始的激发态量子退火。通过使用驱动量子系统的有效能量本征态，这种反直觉的方法成为可能。为了证明这一概念，我们使用Kerr非线性参量振荡器网络，通过适当设置振荡器的初始失谐频率，我们可以在网络的真空状态下开始激发态量子退火。通过对四个振荡器的数值模拟，我们表明，本方法可以解决由于能量隙闭合而无法通过标准基态量子退火获得最优解的一些困难实例。在这种方法中，宁可利用在能隙闭合点的非绝热转变。我们还表明，与以物理激发（即非真空）态开始的量子退火相比，这种方法对预期的耗散误差具有鲁棒性。这些结果为量子计算和驱动量子系统开辟了新的可能性。与以物理激发（即非真空）状态开始的量子退火相比。这些结果为量子计算和驱动量子系统开辟了新的可能性。与以物理激发（即非真空）状态开始的量子退火相比。这些结果为量子计算和驱动量子系统开辟了新的可能性。