Space-time tradeoff for sparse quantum state preparation

2025/06/20 by Luo, Jingquan, Li, Guanzhong, Li, Lvzhou · 3 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.2506.16964

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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((nd log m)/(m log m/n) + log nd) using m≥ 6n ancillary qubits, which achieves the current best trade-off between depth and ancilla number. In particular, when m = Θ((nd)/(log d)), our result recovers the optimal circuit depth Θ(log nd) given in \hyperlinkcite.zhang2022quantum[Phys. Rev. Lett., 129, 230504(2022)], but using significantly fewer gates and ancillary qubits.

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