  Adiabatic quantum computing has demonstrated how quantum Zeno can be used to
construct quantum optimisers. However, much less work has been done to
understand how more general Zeno effects could be used in a similar setting. We
use a construction based on three state systems rather than directly in qubits,
so that a qubit can remain after projecting out one of the states. We find that
our model of computing is able to recover the dynamics of a transverse field
Ising model, several generalisations are possible, but our methods allow for
constraints to be implemented non-perturbatively and does not need tunable
couplers, unlike simple transverse field implementations. We further discuss
how to implement the protocol physically using methods building on STIRAP
protocols for state transfer. We find a substantial challenge, that settings
defined exclusively by measurement or dissipative Zeno effects do not allow for
frustration, and in these settings pathological spectral features arise leading
to unfavorable runtime scaling. We discuss methods to overcome this challenge
for example including gain as well as loss as is often done in optical Ising
machines.
