Quantum Carry-Save Arithmetic

TL;DR

This paper introduces a quantum carry-save arithmetic method that enables faster modular arithmetic computations for quantum algorithms like Shor's, significantly reducing gate delay at the expense of more qubits.

Contribution

It adapts classical carry-save techniques to quantum computing, achieving more efficient quantum arithmetic operations for large-scale algorithms.

Findings

Reduces quantum gate delay from O(N^3) to O(N log N)

Increases qubit requirements from O(N) to O(N^2)

Enables bit-parallel evaluation of quantum arithmetic elements

Abstract

This paper shows how to design efficient arithmetic elements out of quantum gates using "carry-save" techniques borrowed from classical computer design. This allows bit-parallel evaluation of all the arithmetic elements required for Shor's algorithm, including modular arithmetic, deferring all carry propagation until the end of the entire computation. This reduces the quantum gate delay from O(N^3) to O(N log N) at a cost of increasing the number of qubits required from O(N) to O(N^2).