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

A Multi-Qubit Quantum Gate Using the Zeno Effect