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The quantum Zeno effect asserts that quantum measurements inhibitsimultaneous unitary dynamics when the "collapse" events are sufficientlystrong and frequent. This applies in the limit of strong continuous measurementor dissipation. It is possible to implement a dissipative control that is knownas "Zeno Dragging", by dynamically varying the monitored observable, and hencealso the eigenstates which are attractors under Zeno dynamics. This is similarto adiabatic processes, in that the Zeno dragging fidelity is highest when therate of eigenstate change is slow compared to the measurement rate. Wedemonstrate here two methods for using such dynamics to achieve control ofquantum systems. The first, which we shall refer to as "shortcut to Zeno", isanalogous to the shortcuts to adiabaticity (counterdiabatic driving) that arefrequently used to accelerate unitary adiabatic evolution. In the secondapproach we apply the Chantasri Dressel Jordan (2013, CDJ) stochastic action,and demonstrate that the extremal-probability readout paths derived from thisare well suited to setting up a Pontryagin-style optimization of the Zenodragging schedule. Implementing these methods on the Zeno dragging of a qubit,we find that both approaches yield the same solution, namely, that the optimalcontrol is a unitary that matches the motion of the Zeno-monitored eigenstate.These methods open up new pathways toward systematically developing dynamiccontrol of Zeno subspaces to realize dissipatively-stabilized quantumoperations.

Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-based Scheduling Optimization