2026-10-28 · arXiv Quantum Physics
arXiv:2510.08267v2 Announce Type: replace
Abstract: 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 ancilla 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 $\Theta(n^2)$ and requires $\Theta(2^n)$ ancilla qubits. The resulting spacetime allocation is $\Theta(2^n)$, which is optimal. Furthermore, we go beyond scaling arguments to precisely quantify the resources needed for any $n$. We illustrate our method through detailed worked examples of both a ``dense'' state and a W-state. Finally, we demonstrate how to combine this method with existing methods to construct hybrid algorithms with varying space and circuit depth complexities.
原文链接：https://arxiv.org/abs/2510.08267
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