Space-time tradeoff for sparse quantum state preparation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918066182422528 |
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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 |
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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 |