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arXiv · 2510.08267

Low-depth measurement-based deterministic quantum state preparation

Roselyn Nmaju·Fiona Speirits·Sarah Croke
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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 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 O(2^n) 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.

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Roselyn Nmaju, Fiona Speirits, Sarah Croke. 2025-10-09. Low-depth measurement-based deterministic quantum state preparation. https://arxiv.org/abs/2510.08267

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