Grover Speedup from Many Forms of the Zeno Effect

Understand

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.