Measurement-Driven Navigation in Many-Body Hilbert Space: Active-Decision Steering

The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements, which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on the go. This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. The target states of highest interest would be those with multipartite entanglement. Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings. We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity. ... mehrWe show the potential of a significant speedup, employing this greedy approach to a broad family of matrix product state targets. For system sizes considered here, an average value of the speedup factor $f$ across this family settles about 20, for some targets even reaching a few thousands. We also identify a subclass of matrix product state targets, including the ground state of the Affleck-Kennedy-Lieb-Tasaki spin chain, for which the value of $f$ increases with system size. In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a quantum state machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This state-machine-based approach can be applied to a more restricted set of targets, where it sometimes offers advantages over the cost-function-based method. We give an example of a $W$-state preparation, which is accelerated with this method by $f≃3.5$, outperforming the greedy protocol for this target.