Certified Quantum Schrödinger Control via Hierarchical Tucker Models

• URL: http://arxiv.org/abs/2603.20168v1
• Date: Fri, 20 Mar 2026 17:46:50 GMT
• Title: Certified Quantum Schrödinger Control via Hierarchical Tucker Models
• Abstract summary: This paper develops a framework for sampled-data feedback control implemented with fixed-rank HT projections.<n>By viewing each truncation as a bounded, rank-dependent of the nominal closed loop, we show that the HT-projected dynamics are practically exponentially stable.
• Score: 2.033424698590539
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: High-dimensional Schrödinger systems arising from tensor-product discretizations suffer from exponential state growth, making direct controller synthesis and real-time closed-loop simulation computationally challenging. Hierarchical Tucker (HT) tensor representations offer scalable low-rank surrogates, but the impact of fixed-rank truncation on closed-loop stability is not well understood. This paper develops a local robustness framework for sampled-data feedback control implemented with fixed-rank HT projections. By viewing each truncation as a bounded, rank-dependent perturbation of the nominal closed loop, and assuming a local phase-invariant contraction certificate together with trajectory-level hierarchical spectral decay, we show that the HT-projected dynamics are practically exponentially stable: trajectories converge to a dimension-independent tube whose radius decreases with the prescribed rank. We further obtain an explicit logarithmic rank-accuracy relation and establish conditions under which controllers designed on the HT-truncated surrogate model retain practical exponential tracking guarantees when deployed on the full system, together with an explicit bound quantifying the resulting surrogate-to-plant mismatch. A compact lattice example demonstrates the applicability of the framework.

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