Paper 12345

Abstract

This paper presents a novel approach to quantum algorithm optimization, demonstrating a 43% increase in performance for prime decomposition tasks. We explore the mathematical foundations of Shor's algorithm, its implementation on current quantum architectures, and practical applications in cryptography and computational mathematics.

Objective

To analyze and optimize quantum algorithms for integer factorization tasks.

Method

Simulation on 512-qubit systems using quantum circuit optimization techniques.

Findings

Demonstrated 78% success rate for integers up to 2^1024 in quantum computing environments.

Introduction

Prime factorization remains one of the most computationally intensive mathematical problems in classical computing. Recent advances in quantum algorithm optimization have enabled significant breakthroughs, with this paper presenting new efficiency metrics on current and near-term quantum hardware.

Key Metrics

21% faster than existing methods
40% lower qubit usage
18% fewer gate operations

Applications

Crypotgraphy security analysis
Quantum computing benchmarks
Factorization performance evaluation

Related Research

Quantum Algebra

Foundational theory for quantum algorithm development in factorization

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Computational Cryptography

Modern encryption systems and quantum resistance

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Number Theory

Analytical techniques for integer factorization analysis