  The Zeno effect, in which repeated observation freezes the dynamics of a
quantum system, stands as an iconic oddity of quantum mechanics. When a
measurement is unable to distinguish between states in a subspace, the dynamics
within that subspace can be profoundly altered, leading to non-trivial
behavior. Here we show that such a measurement can turn a non-interacting
system with only single-qubit control into a two- or multi-qubit entangling
gate, which we call a Zeno gate. The gate works by imparting a geometric phase
on the system, conditioned on it lying within a particular nonlocal subspace.
We derive simple closed-form expressions for the gate fidelity under a number
of non-idealities and show that the gate is viable for implementation in
circuit and cavity QED systems. More specifically, we illustrate the
functioning of the gate via dispersive readout in both the Markovian and
non-Markovian readout regimes, and derive conditions for longitudinal readout
to ideally realize the gate.
