Scalable Generic State Preparation through Tensor Cross Interpolation and Binary Trees

Kurzfassung

Efficient preparation of generic quantum states remains a major computational bottleneck in many quantum algorithms and protocols. In this work, we employ a maximally expressive recursive circuit capable of representing arbitrary pure quantum states exactly. We then introduce two complementary methods, both based on an intermediate binary-tree representation, that systematically exploit structure in the target data across multiple scales to reduce circuit depth under realistic connectivity constraints. The first method uses a boolean representation of the circuit parameters and connects the optimization problem to classical logic simplification techniques. The second method, based on tensor networks, is inherently scalable to large system sizes and particularly effective for structured high-dimensional functions. In particular, it uses tensor cross interpolation to construct tensor-train representations of queryable functions beyond direct memory storage and maps them onto sequences of single-qubit and controlled rotations. This framework offers a transparent, deterministic, highly tunable, scalable and general purpose data encoding method, which outperforms other methods in literature, and offers many distinct paths forward in this critical bottleneck on the road to quantum advantage.