Measurement-driven navigation in many-body Hilbert space

The challenge of preparing a system in a designated state spans various areas of quantum physics. To complete this task, one can employ quantum control through a sequence of generalized measurements. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go, with a possibility for accelerated performance.

We study the potential of such active measurement-driven control as applied to many-body state preparation. For advantageous decision-making, we offer Hilbert space orientation techniques, comparable to those used in navigation. The first such method is to orient the active protocol towards the maximization of a cost function, such as the target state fidelity. We show the potential of an O(10)-fold speedup applying this approach to AKLT states of 3-6 spins. The complementary technique is to map out the measurement actions onto a quantum version of Finite State Machine. A decision-making protocol can be based on such representation, using semiclassical heuristics. We give an example of the W-state preparation, which can be accelerated with this method by a factor of O(10).