标题： 基于残数数系的分布式量子乘法 显示英文标题

标题： Residue Number System (RNS) based Distributed Quantum Multiplication

摘要： 量子态的乘法是量子算法和应用中常用的功能或子程序，使得量子乘法器成为量子算术中的关键组件。 然而，量子乘法器电路存在较高的Toffoli深度和T门使用量，这最终影响了它们的可扩展性和在量子计算机上的适用性。 为了解决这些问题，我们提出利用基于剩余数系统（RNS）的分布式量子乘法，该方法在量子计算机或任务上执行多个量子模乘电路，具有较低的Toffoli深度和T门使用量。 为此，我们提出了一种量子减1模$(2^n+1)$乘法器的设计，这是基于RNS的分布式量子乘法的关键组件。 我们提供了量子资源使用的估计，并将其与现有非分布式量子乘法器在6到16量子比特输出规模下的结果进行了比较。 我们的比较分析显示，Toffoli深度最多降低了46.018%，T门数量减少了34.483%至86.25%。 显示英文摘要

摘要： 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%.