Quantum Circuits for Toom-Cook Multiplication

TL;DR

This paper presents optimized quantum circuits for integer multiplication based on the Toom-Cook algorithm, achieving better asymptotic bounds than previous methods by analyzing recursive structures and employing reversible pebble games.

Contribution

It introduces efficient quantum circuits for Toom-Cook multiplication with improved bounds on gate count and qubits, advancing quantum multiplication techniques.

Findings

Reduced Toffoli gate count compared to prior methods

Lower qubit requirements through uncomputing intermediate results

Superior asymptotic performance over schoolbook and Karatsuba algorithms

Abstract

In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds are further improved by employing reversible pebble games through uncomputing the intermediate results. The asymptotic bounds for different performance metrics of the proposed quantum circuit are superior to the prior implementations of multiplier circuits using schoolbook and Karatsuba algorithms.