[Paper Review] Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Yaroslav Herasymenko, I. V. Gornyi+1 more|arXiv (Cornell University)|Nov 17, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces an active-decision framework for measurement-driven quantum state preparation in many-body systems, using real-time feedback from measurements to steer toward target entangled states. It achieves speedups of up to 20× (and up to thousands for specific states) by employing greedy fidelity maximization and a Quantum State Machine approach, with demonstrated advantages for W-states and matrix product states.

ABSTRACT

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. 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. We 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, 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, sometimes offering advantages over the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by $f\simeq3.5$, outperforming the greedy protocol for this target.

Motivation & Objective

• To develop a general framework for active, measurement-driven navigation in many-body Hilbert space toward target quantum states.
• To address the challenge of preparing complex, genuinely multipartite entangled states using only generalized measurements with physically feasible couplings.
• To improve on passive measurement protocols by incorporating real-time decision-making based on measurement outcomes.
• To identify physically realizable system-detector couplings through parent Hamiltonian construction.
• To compare and contrast two decision-making strategies: greedy fidelity maximization and Quantum State Machine-based navigation.

Proposed method

• Construct physically feasible system-detector couplings using parent Hamiltonian techniques to ensure compatibility with local interactions.
• Implement a greedy active-decision protocol that selects subsequent measurements to maximize the target state fidelity at each step.
• Map measurement actions onto a coarse-grained Quantum State Machine (QSM), representing transitions between states in a semiclassical graph structure.
• Use semiclassical heuristics to guide decisions in the QSM framework, enabling navigation without full Hilbert space tracking.
• Apply both methods to benchmark targets, including Matrix Product States (MPS) and W-states, to evaluate performance.
• Quantify speedup factors by comparing active protocols to passive counterparts, using fidelity and runtime as metrics.

Experimental results

Research questions

• RQ1 Can active decision-making in measurement-only protocols significantly accelerate the preparation of entangled many-body states?
• RQ2 How do greedy fidelity-based strategies compare to QSM-based strategies in terms of speedup and robustness for different target states?
• RQ3 What are the physically realizable system-detector couplings that enable efficient measurement-driven steering?
• RQ4 Does the speedup of active protocols scale favorably with system size for specific classes of entangled states?
• RQ5 Can QSM-based navigation outperform greedy protocols for certain targets, such as W-states?

Key findings

• The greedy fidelity-based protocol achieves an average speedup factor of approximately 20 across a broad family of Matrix Product State targets.
• For certain MPS targets, including the AKLT ground state, the speedup factor increases with system size, indicating scalability.
• The QSM-based method achieves a speedup of $ f_{\mathrm{QSM}} = 3.5 $ for W-state preparation, outperforming the greedy approach ($ f_{\mathrm{greedy}} = 3.1 $) for this target.
• The QSM approach reduces sensitivity to measurement imperfections due to its coarse-grained, semiclassical representation of state transitions.
• Active steering can overcome limitations of passive protocols, potentially enabling access to target states otherwise unreachable under fixed coupling constraints.
• The framework is generalizable and opens pathways for integrating machine learning, Hamiltonian dynamics, and automated QSM construction in future work.