DISTRIBUTED QUANTUM MULTIPLICATION WITH HIGH PERFORMANCE MAKING USE OF RNS

A key component of quantum algorithms is the efficient multiplication of quantum states; nevertheless, the scalability of traditional quantum multipliers on quantum hardware is frequently limited by high Toffoli depth and excessive T gate utilization. This research introduces a distributed quantum multiplication framework based on the Residue Number System (RNS) that performs numerous quantum modulo multiplication operations across different quantum processors or computational tasks. We present a Quantum Diminished-1 Modulo (2⋅+1) Multiplier inside this framework, which is a crucial element that improves the effectiveness of RNS-based distributed multiplication. For outputs between 6 and 16 qubits, we present a thorough examination of the quantum resource requirements and contrast the suggested method with a traditional non-distributed quantum multiplier. The results underscore the promise of the suggested strategy for scalable and resource-efficient quantum arithmetic, showing reductions of up to 46.02% in Toffoli depth and 34.48% to 86.25% in T gate count.