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

The challenge of preparing a system in designated state spans diverse facets quantum mechanics. To complete this task steering states, one can employ control through sequence generalized measurements, which direct the towards target state. In an active version protocol, obtained measurement readouts are used to adjust protocol on go. This enables sped-up performance relative passive where no adjustments included. work, we consider such measurement-driven as applied challenging case many-body systems. states highest interest would be those with multipartite entanglement. Such preparation measurement-based is limited by natural constraints for system-detector couplings. We develop framework finding physically feasible couplings, based parent Hamiltonian construction. For helpful decision-making strategies, offer Hilbert-space-orientation techniques, comparable navigation. first tie active-decision greedy accumulation cost function, fidelity. show potential significant speedup, employing approach broad family matrix product targets. sizes considered here, average value speedup factor f across settles about 20, some targets even reaching few thousands. also identify subclass targets, including ground Affleck-Kennedy-Lieb-Tasaki spin chain, increases size. addition approach, second wayfinding technique map out available actions onto machine. A representation, using semiclassical heuristics. state-machine-based more restricted set it sometimes offers advantages over cost-function-based method. give example W-state preparation, accelerated method f≃3.5, outperforming target.3 MoreReceived 24 December 2021Revised 10 October 2022Accepted May 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020347Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) and published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement productionQuantum controlQuantum engineeringWeak values & weak measurementsTechniquesApproximation methods systemsQuantum InformationCondensed Matter, Materials Applied Physics