Space-time tradeoff for sparse quantum state preparation

• URL: http://arxiv.org/abs/2506.16964v1
• Date: Fri, 20 Jun 2025 12:52:05 GMT
• Title: Space-time tradeoff for sparse quantum state preparation
• Authors: Jingquan Luo, Guanzhong Li, Lvzhou Li,
• Abstract summary: We prove that any $n$-qubit $d$-spare quantum state can be prepared by a quantum circuit with depth $Oleft(fracnd log mm log m/n + log ndright)$ using $mgeq 6n$ ancillary qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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