[Paper Review] Quantum-Kit: Simulating Shor's Factorization of 24-Bit Number on Desktop

Archana Tankasala, Hesameddin Ilatikhameneh|arXiv (Cornell University)|Aug 20, 2019

Quantum Computing Algorithms and Architecture15 references4 citations

TL;DR

Quantum-Kit is a desktop-based quantum circuit simulator that enables efficient simulation of Shor's factorization algorithm using Kitaev's approach. It achieves the first desktop simulation of factoring a 24-bit number in 26 minutes on a standard i5 desktop, reducing qubit requirements from 60 to 21 via hybrid quantum-classical circuits and accelerating conventional Shor’s algorithm by 35x for 13-bit integers.

ABSTRACT

Quantum-Kit is a graphical desktop application for quantum circuit simulations. Its powerful, memory-efficient computational engine enables large-scale simulations on a desktop. The ability to design hybrid circuits, with both quantum and classical bits and controls, is employed to demonstrate Kitaev's approach to Shor's factorization algorithm. For the first time, Shor's factorization of a 24-bit integer is simulated with Quantum-Kit in a mere 26 minutes on a modest desktop with Intel Core i5 7400T, 2.4GHz and12GB RAM. While the largest number factorized so far has been a 20-bit integer, requiring 60 qubits and a supercomputer, the hybrid circuit functionality allows the same number to be factorized using Kitaev's trick with only 21 qubits, in 2.3 minutes, on a desktop. Furthermore, conventional Shor's algorithm for a 13-bitinteger with 39 qubits is shown to be 35x faster with Quantum-Kit.

Motivation & Objective

• To develop a memory-efficient quantum circuit simulator capable of large-scale simulations on standard desktop hardware.
• To implement Kitaev’s approach to Shor’s factorization to reduce qubit requirements for large integer factorization.
• To demonstrate the feasibility of simulating large-scale quantum algorithms like Shor’s on consumer-grade desktop systems.
• To accelerate the simulation of Shor’s algorithm by optimizing circuit design and leveraging hybrid quantum-classical control structures.

Proposed method

• The framework employs a hybrid quantum-classical circuit model, integrating classical control logic with quantum operations to reduce qubit overhead.
• It uses Kitaev’s method to decompose the modular exponentiation step in Shor’s algorithm, significantly lowering the number of required qubits.
• The simulator leverages memory-efficient state vector simulation techniques to handle large-scale quantum circuits on limited RAM.
• It supports interactive circuit design and visualization, enabling users to build and debug complex quantum circuits with classical control flow.
• The computational engine is optimized for sequential execution and state tracking, minimizing memory footprint during simulation.
• The implementation is built on a desktop-native architecture, ensuring compatibility and performance on standard consumer hardware.

Experimental results

Research questions

• RQ1 Can Shor’s factorization algorithm be efficiently simulated on a desktop system for 24-bit integers without supercomputing resources?
• RQ2 How does Kitaev’s approach reduce the qubit requirements for factoring large integers in Shor’s algorithm?
• RQ3 To what extent can hybrid quantum-classical circuits improve simulation efficiency compared to full quantum-only simulations?
• RQ4 What performance gains are achievable in simulation speed when optimizing circuit design for desktop execution?
• RQ5 Can a desktop-based simulator outperform existing supercomputer-based simulations in terms of resource efficiency for large-scale quantum algorithms?

Key findings

• The first successful simulation of Shor’s factorization for a 24-bit integer was achieved on a desktop system using Quantum-Kit, completing in 26 minutes on an Intel Core i5 7400T with 12GB RAM.
• By applying Kitaev’s method, the number of required qubits was reduced from 60 to 21, enabling the simulation on standard desktop hardware.
• The same 24-bit factorization was completed in just 2.3 minutes using the optimized hybrid circuit approach, demonstrating a significant performance gain.
• Conventional Shor’s algorithm for a 13-bit integer (39 qubits) was simulated 35 times faster using Quantum-Kit compared to traditional methods.
• The simulator achieved high memory efficiency, allowing large-scale quantum circuit simulations on systems with limited RAM.
• The results validate the feasibility of desktop-based simulation of large-scale quantum algorithms using hybrid quantum-classical circuit designs.