Space-time tradeoff for sparse quantum state preparation

Fuente: arXiv
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Main Authors: Luo, Jingquan, Li, Guanzhong, Li, Lvzhou
Format: Preprint
Published: 2025
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author Luo, Jingquan
Li, Guanzhong
Li, Lvzhou
author_facet Luo, Jingquan
Li, Guanzhong
Li, Lvzhou
contents 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 $m = Θ({\frac{nd}{\log d}})$, our result recovers the optimal circuit depth $Θ(\log nd)$ given in \hyperlink{cite.zhang2022quantum}{[Phys. Rev. Lett., 129, 230504(2022)]}, but using significantly fewer gates and ancillary qubits.
format Preprint
id arxiv_https___arxiv_org_abs_2506_16964
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Space-time tradeoff for sparse quantum state preparation
Luo, Jingquan
Li, Guanzhong
Li, Lvzhou
Quantum Physics
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 $m = Θ({\frac{nd}{\log d}})$, our result recovers the optimal circuit depth $Θ(\log nd)$ given in \hyperlink{cite.zhang2022quantum}{[Phys. Rev. Lett., 129, 230504(2022)]}, but using significantly fewer gates and ancillary qubits.
title Space-time tradeoff for sparse quantum state preparation
topic Quantum Physics
url https://arxiv.org/abs/2506.16964