  We present a framework for quantum computation, similar to Adiabatic Quantum
Computation (AQC), that is based on the quantum Zeno effect. By performing
randomised dephasing operations at intervals determined by a Poisson process,
we are able to track the eigenspace associated to a particular eigenvalue.
  We derive a simple differential equation for the fidelity, leading to general
theorems bounding the time complexity of a whole class of algorithms. We also
use eigenstate filtering to optimise the scaling of the complexity in the error
tolerance $\epsilon$.
  In many cases the bounds given by our general theorems are optimal, giving a
time complexity of $O(1/\Delta_m)$ with $\Delta_m$ the minimum of the gap. This
allows us to prove optimal results using very general features of problems,
minimising the problem-specific insight necessary.
  As two applications of our framework, we obtain optimal scaling for the
Grover problem (i.e.\ $O(\sqrt{N})$ where $N$ is the database size) and the
Quantum Linear System Problem (i.e.\ $O(\kappa\log(1/\epsilon))$ where $\kappa$
is the condition number and $\epsilon$ the error tolerance) by direct
applications of our theorems.
