Residue Number System (RNS) based Distributed Quantum Addition

TL;DR

This paper introduces a distributed quantum addition method using Residue Number System (RNS) to improve noise resilience and scalability on NISQ-era quantum computers, demonstrated through simulations on Quantinuum's hardware.

Contribution

It proposes RNS-based distributed quantum adders and the QSMART tool for optimized adder generation, enhancing noise resilience and scalability in quantum arithmetic.

Findings

RNS-based distributed quantum addition shows 11.36% to 133.15% higher output probability.

The approach enables scalable quantum addition beyond 20 qubits.

Simulations confirm improved noise fidelity over non-distributed adders.

Abstract

Quantum Arithmetic faces limitations such as noise and resource constraints in the current Noisy Intermediate Scale Quantum (NISQ) era quantum computers. We propose using Distributed Quantum Computing (DQC) to overcome these limitations by substituting a higher depth quantum addition circuit with Residue Number System (RNS) based quantum modulo adders. The RNS-based distributed quantum addition circuits possess lower depth and are distributed across multiple quantum computers/jobs, resulting in higher noise resilience. We propose the Quantum Superior Modulo Addition based on RNS Tool (QSMART), which can generate RNS sets of quantum adders based on multiple factors such as depth, range, and efficiency. We also propose a novel design of Quantum Diminished-1 Modulo (2n + 1) Adder (QDMA), which forms a crucial part of RNS-based distributed quantum addition and the QSMART tool. We demonstrate the higher noise resilience of the Residue Number System (RNS) based distributed quantum addition by conducting simulations modeling Quantinuum's H1 ion trap-based quantum computer. Our simulations demonstrate that RNS-based distributed quantum addition has 11.36% to 133.15% higher output probability over 6-bit to 10-bit non-distributed quantum full adders, indicating higher noise fidelity. Furthermore, we present a scalable way of achieving distributed quantum addition higher than limited otherwise by the 20-qubit range of Quantinuum H1.