Core Concepts
Developing techniques to measure quantum integer factorization performance using Shor's algorithm is crucial for assessing practical feasibility.
Abstract
Abstract:
Importance of accurately measuring quantum algorithms' performance.
Analyzing time required for integer factorization tasks using Shor’s algorithm.
Impact of parameter pre-selection on success rate and scalability.
Introduction:
Significance of quantum technologies in cybersecurity.
Threat posed by quantum algorithms like Shor’s and Grover’s.
Focus on the potential threat landscape with current quantum computing resources.
Theoretical Background:
Overview of Shor’s algorithm and its steps.
Explanation of Quantum Fourier Transform and its role in various algorithms.
Introduction to Matrix Product State quantum simulation.
Integer Factorization Using Selected Parameter:
Role of random parameters in Shor's algorithm efficiency.
Pre-selection strategy for parameter a to enhance scalability.
Entanglement Analysis for MPS:
Importance of register order for efficient simulation.
Performance of Shor’s Algorithm at Scale:
Comparison between pre-selected and random selection scenarios.
Conclusion & Future Works:
Evaluation of integer factorization scalability using Matrix Product State method.
Importance of parameter selection methodology for optimal performance.
Stats
"With support for up to 100 qubits, it facilitated the evaluation of Shor’s algorithm for integer factorization of numbers up to 24 bits."
"The memory requirements for the computation increase proportionally to χ2n."
"When a is pre-selected with a minimum period of r = 2, 8 shots were sufficient to factorize all given input numbers."