Computational complexity theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications.
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theoretical framework for evaluating the algorithm
This field provides the tools to compare the efficiency of Shor's algorithm against classical factoring algorithms like the General Number Field Sieve.
Theoretical foundation for defining quantum advantage
Quantum supremacy relies on the gap between complexity classes, specifically demonstrating that quantum circuits can solve problems outside the reach of classical polynomial-time algorithms.