Fast Quantum Modular Exponentiation Architecture for Shor's Factorization Algorithm

Understand

We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm.

• The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build more complex arithmetic blocks: quantum multiplier/accumulators by constants and quantum dividers by constants.
• These arithmetic blocks are effectively architected into a generic modular quantum multiplier which is the fundamental block for modular exponentiation circuit, the most computational intensive part of Shor's algorithm.
• The proposed modular exponentiation circuit has a depth of about $2000n^{2}$ and requires $9n+2$ qubits, where $n$ is the number of bits of the classical number to be factored.