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

The Quantum Zeno Effect asserts that quantum measurements inhibit simultaneous unitary dynamics, when the "collapse" events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It is possible to implement a dissipative control that is known as "Zeno Dragging", by dynamically varying the observable monitored, and hence the eigenstates which are attractors under Zeno dynamics; this is similar to adiabatic processes, in that the Zeno dragging fidelity is highest when the rate of eigenstate change is slow compared to the measurement rate. We demonstrate here two methods of interest in this context. The first, which we shall refer to as 'shortcut to Zeno', is analogous to the shortcuts to adiabaticity (counterdiabatic driving) that are frequently used to accelerate unitary adiabatic controls. In the second approach we apply the Chantasri Dressel Jordan (2013, CDJ) stochastic action, and demonstrate that the extremal–probability readout paths derived from it are well suited to setting up a Pontryagin–style optimization of the Zeno dragging schedule. Implementing these methods on Zeno dragging of a qubit, we find that both approaches yield the same solution, namely, that the optimal control is a unitary that matches the motion of the Zeno–monitored eigenstate.