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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Rini Wisnu Wardhani
Politeknik Siber dan Sandi Negara
Mathematics

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Toward Optimal Quantum Multipliers: Space–Time Efficiency and Asymptotic Bounds for Advanced Toom–Cook Methods Rini Wisnu Wardhani; Dedy Septono Catur Putranto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41908

Abstract

This paper studies the asymptotic bounds of quantum resources required for high-degree multiplication based on the Toom–Cook algorithm. This work extends prior investigations on high- and half-degree quantum multiplication and proposes an optimized Toom–Cook 25.5-way quantum multiplication architecture to establish optimal asymptotic bounds on quantum resource consumption for Toom–Cook-based multiplication schemes. We provide asymptotic expressions for qubit complexity, Toffoli gate count, and Toffoli depth. The proposed Toom–Cook 25.5-way architecture achieves improved asymptotic performance, requiring a qubit count of n1.176, approximately 648nlog2651 − 666n Toffoli count, and n1.03025 Toffoli depth. Compared with existing classical and quantum Toom–Cook-based methods, the proposed 25.5-way Toom–Cook algorithm achieves lower asymptotic complexity and reduced quantum resource costs, yielding tighter bounds for optimal quantum multiplication.
Co-Authors Dedy Septono Catur Putranto