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  • Open Access

Determinate arbitrary quantum state engineering through one-dimensional quantum walks

Yu Wang1,*, Meng Li2,†, and Yuan-Yuan Zhao3,‡

  • *Contact athor: wangyu@bimsa.cn
  • †Contact athor: limeng2021@ict.ac.cn
  • ‡Contact athor: zhaoyuanyuan1@quantumsc.cn
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Phys. Rev. Research 7, 023252 – Published 11 June, 2025

DOI: https://doi.org/10.1103/2frm-2v6m

Abstract

Efficient generation of arbitrary superposed quantum states in high-dimensional systems is crucial for various quantum technologies but remains fundamentally challenging because of the intricate and extensive parameter control. In this work, we propose a generalized discrete one-dimensional quantum walk model with time- and position-dependent coin operations, and varied shift lengths. This approach enables deterministic and direct preparation of any qudit state |ϕ〉=∑k=0d−1ak|k〉 using binary or ternary tree structures, without solving quadratic equations. Our method requires only O(logd) steps and O(d) coin operations, significantly reducing the resource requirements compared to the previous approach of O(d) steps and O(d2) coin operations. Additionally, we propose an experimental scheme based on successive interferometers, demonstrating that our method is compatible with current state-of-the-art experimental technologies. This efficient method for preparing quantum superposition states lays a foundation for advancing quantum technologies, with broad applications in quantum information processing.

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Phys. Rev. Research 7, 023252– Published 11 June, 2025
  • Received 31 October 2024
  • Accepted 29 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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