It has previously been established that adiabatic quantum computation, operating based on a continuous Zeno effect due to dynamical phases between eigenstates, is able to realise an optimal Grover-like quantum speedup. In other words, is able to solve an unstructured search problem with the same $\sqrt{N}$ scaling as Grover's original algorithm. A natural question is whether other manifestations of the Zeno effect can also support an optimal speedup in a physically realistic model (through direct analogue application rather than indirectly by supporting a universal gateset). In this paper we show that they can support such a speedup, whether due to measurement, decoherence, or even decay of the excited state into a computationally useless state. Our results also suggest a wide variety of methods to realise speedup which do not rely on Zeno behaviour. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained: one based on phase kicks, containing adiabatic computation and continuous-time quantum walks; one based on dephasing and measurement; and finally one based on destruction of the amplitude within the excited state, for which we are not aware of any previous results. These results suggest that there may be exciting opportunities for new paradigms of analog quantum computing based on these effects.

中文翻译：

---

多种形式的 Zeno 效果的 Grover 加速


先前已经确定，绝热量子计算基于本征态之间动力学相位导致的连续芝诺效应运行，能够实现最佳的 Grover 类量子加速。换句话说，能够使用与 Grover 的原始算法相同的 $\sqrt{N}$ 缩放来解决非结构化搜索问题。一个自然而然的问题是，Zeno 效应的其他表现形式是否也可以在物理真实模型中支持最佳加速（通过直接模拟应用，而不是间接通过支持通用门集）。在本文中，我们展示了它们可以支持这种加速，无论是由于测量、退相干，还是由于激发态衰减到计算无用的状态。我们的结果还表明了不依赖于 Zeno 行为的多种方法来实现加速。我们将这些算法分为三个系列，以促进对如何获得加速的结构化理解：一个基于相位突起，包含绝热计算和连续时间量子游走;一个基于去相和测量;最后一种是基于激发态内振幅的破坏，我们不知道之前的任何结果。这些结果表明，基于这些效应的模拟量子计算新范式可能存在令人兴奋的机会。