Adaptive Tensor Network Sampling for Quantum Optimal Control

TL;DR

This paper introduces a gradient-free tensor network sampling method for quantum optimal control, enabling efficient search in complex, high-dimensional control landscapes with promising empirical results.

Contribution

It proposes a novel tensor network sampling heuristic for discrete quantum control, improving search efficiency without gradient information.

Findings

Method shows stable convergence across benchmark problems.

Competitive performance compared to existing gradient-free methods.

Effective in tasks like state transfer and gate implementation.

Abstract

Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly fall into two categories: gradient-based and gradient-free algorithms. The associated optimization landscape is often high-dimensional, non-convex, and populated by numerous local minima, making efficient gradient-free search strategies essential. To address this, we introduce a gradient-free matrix product state/tensor train (MPS/TT) sampling heuristic for discrete quantum optimal control. In our approach, the MPS defines a score function over the space of discrete control parameters, which in turn induces a sampling distribution over candidate control sequences. This distribution is iteratively refined through selection of better performing sequences and local tensor updates to bias the search toward high-performing sequences. We evaluate the method on a range of benchmark problems, including single-qubit state transfer, Bell-pair preparation, qutrit gate implementation, and open-system population transfer. Across these tasks, the method exhibits stable convergence behavior and competitive empirical performance relative to established gradient-free baselines. These results suggest that tensor network sampling offers a viable heuristic framework for discrete quantum control.