Low-depth measurement-based deterministic quantum state preparation

We present a low-depth amplitude encoding method for arbitrary quantum state preparation. Building on the foundation of an existing divide-and-conquer algorithm, we propose a method to disentangle the ancillary qubits from the final state. Our method is measurement-based but deterministic, and offers an alternative approach to existing state preparation algorithms. It has circuit depth O(n), which is known to be optimal, and O2ⁿ ancilla qubits, which is close to optimal. We illustrate our method through detailed worked examples of both a "dense" state and a W-state. We discuss extensions to the algorithm resetting qubits mid-circuit, and construct hybrid algorithms with varying space and circuit depth complexities.