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arXiv · 2506.16964

Space-time tradeoff for sparse quantum state preparation

Jingquan Luo·Guanzhong Li·Lvzhou Li
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Abstract

In this work, we investigate the trade-off between the circuit depth and the number of ancillary qubits for preparing sparse quantum states. We prove that any $n$-qubit $d$-spare quantum state (i.e., it has only $d$ non-zero amplitudes) can be prepared by a quantum circuit with depth $O\left(\frac{nd \log m}{m \log m/n} + \log nd\right)$ using $m\geq 6n$ ancillary qubits, which achieves the current best trade-off between depth and ancilla number. In particular, when $m = \Theta({\frac{nd}{\log d}})$, our result recovers the optimal circuit depth $\Theta(\log nd)$ given in \hyperlink{cite.zhang2022quantum}{[Phys. Rev. Lett., 129, 230504(2022)]}, but using significantly fewer gates and ancillary qubits.

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Jingquan Luo, Guanzhong Li, Lvzhou Li. 2025-06-20. Space-time tradeoff for sparse quantum state preparation. https://arxiv.org/abs/2506.16964

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