Space-Optimized and Experimental Implementations of Regev's Quantum Factoring Algorithm

Fuente: arXiv
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Hauptverfasser: Yang, Wentao, Yan, Bao, Zheng, Muxi, Lu, Quanfeng, Wei, Shijie, Long, Gui-Lu
Format: Preprint
Veröffentlicht: 2025
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author Yang, Wentao
Yan, Bao
Zheng, Muxi
Lu, Quanfeng
Wei, Shijie
Long, Gui-Lu
author_facet Yang, Wentao
Yan, Bao
Zheng, Muxi
Lu, Quanfeng
Wei, Shijie
Long, Gui-Lu
contents The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based post-processing, but introduces substantial space overhead and lacks practical implementations. Here, we propose a qubit reuse method by intermediate-uncomputation that significantly reduces the space complexity of Regev's algorithm, inspired by reversible computing. Our basic strategy lowers the cost from \( O(n^{3/2}) \) to \( O(n^{5/4}) \), and refined strategies achieve \( O(n \log n) \)which is a space lower bound within this model. Simulations demonstrate the resulting time-space trade-offs and resource scaling. Moreover, we construct and compile quantum circuits that factor \( N = 35 \), verifying the effectiveness of our method through noisy simulations. A more simplified experimental circuit for Regev's algorithm is executed on a superconducting quantum computer, with lattice-based post-processing successfully retrieving the factors. These results advance the practical feasibility of Regev-style quantum factoring and provide guidance for future theoretical and experimental developments.
format Preprint
id arxiv_https___arxiv_org_abs_2511_18198
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Space-Optimized and Experimental Implementations of Regev's Quantum Factoring Algorithm
Yang, Wentao
Yan, Bao
Zheng, Muxi
Lu, Quanfeng
Wei, Shijie
Long, Gui-Lu
Quantum Physics
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based post-processing, but introduces substantial space overhead and lacks practical implementations. Here, we propose a qubit reuse method by intermediate-uncomputation that significantly reduces the space complexity of Regev's algorithm, inspired by reversible computing. Our basic strategy lowers the cost from \( O(n^{3/2}) \) to \( O(n^{5/4}) \), and refined strategies achieve \( O(n \log n) \)which is a space lower bound within this model. Simulations demonstrate the resulting time-space trade-offs and resource scaling. Moreover, we construct and compile quantum circuits that factor \( N = 35 \), verifying the effectiveness of our method through noisy simulations. A more simplified experimental circuit for Regev's algorithm is executed on a superconducting quantum computer, with lattice-based post-processing successfully retrieving the factors. These results advance the practical feasibility of Regev-style quantum factoring and provide guidance for future theoretical and experimental developments.
title Space-Optimized and Experimental Implementations of Regev's Quantum Factoring Algorithm
topic Quantum Physics
url https://arxiv.org/abs/2511.18198