Residue Number System (RNS) based Distributed Quantum Multiplication

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%.