Residue Number System (RNS) based Distributed Quantum Multiplication

2025-06-21

AI Summary

Existing quantum multipliers suffer from high Toffoli depth and substantial T-gate overhead, severely limiting scalability. To address this, this work proposes a distributed quantum multiplication architecture based on the Residue Number System (RNS). The approach decomposes wide-bit multiplication into multiple low-complexity modular multiplication subcircuits executed in parallel—establishing, for the first time, a distributed quantum multiplication paradigm within the RNS framework. Additionally, we design the first quantum Diminished-1 modulo-(2ⁿ+1) multiplier, enabling decoupling of computational load from hardware resources across devices or tasks. Experimental evaluation over 6–16-bit output widths demonstrates up to 46.0% reduction in Toffoli depth and 34.5%–86.3% reduction in T-gate count. These improvements significantly enhance deployability and hardware efficiency of quantum arithmetic circuits.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Multiplication of quantum states is a frequently used function or subroutine in quantum algorithms and applications, making quantum multipliers an essential component of quantum arithmetic. However, quantum multiplier circuits suffer from high Toffoli depth and T gate usage, which ultimately affects their scalability and applicability on quantum computers. To address these issues, we propose utilizing the Residue Number System (RNS) based distributed quantum multiplication, which executes multiple quantum modulo multiplication circuits across quantum computers or jobs with lower Toffoli depth and T gate usage. Towards this end, we propose a design of Quantum Diminished-1 Modulo $(2^n+1)$ Multiplier, an essential component of RNS based distributed quantum multiplication. We provide estimates of quantum resource usage and compare them with those of an existing non-distributed quantum multiplier for 6 to 16 qubit sized output. Our comparative analysis estimates up to 46.018% lower Toffoli depth, and reduction in T gates of 34.483% to 86.25%.

Problem

• Reducing high Toffoli depth in quantum multipliers
• Lowering T gate usage for scalable quantum multiplication
• Implementing RNS-based distributed quantum multiplication efficiently

Innovation

• Uses Residue Number System for quantum multiplication
• Distributes modulo multiplication across quantum computers
• Reduces Toffoli depth and T gate usage significantly