Quantum Computing

9.

Applications and Impact

9.1.

9.1.1.

Quantum Attacks on Classical Cryptography

9.1.1.1.

9.1.1.2.

Discrete Logarithm Problem

9.1.1.3.

Elliptic Curve Cryptography

9.1.2.

Quantum Key Distribution (QKD)

9.1.2.1.

9.1.2.2.

9.1.2.3.

Security Proofs

9.1.2.4.

Practical Implementations

9.1.3.

Post-Quantum Cryptography (PQC)

9.1.3.1.

Lattice-Based Cryptography

9.1.3.2.

Code-Based Cryptography

9.1.3.3.

Multivariate Cryptography

9.1.3.4.

Hash-Based Signatures

9.1.3.5.

NIST Standardization Process

9.2.

9.2.1.

Quantum Chemistry

9.2.1.1.

Molecular Energy Calculations

9.2.1.2.

Electronic Structure Problems

9.2.1.3.

9.2.1.4.

Catalyst Design

9.2.1.5.

Protein Folding

9.2.2.

Materials Science

9.2.2.1.

Modeling Quantum Materials

9.2.2.2.

Superconductivity

9.2.2.3.

Magnetic Materials

9.2.2.4.

Phase Transitions

9.2.3.

High-Energy Physics

9.2.3.1.

Lattice Gauge Theories

9.2.3.2.

Particle Interactions

9.2.3.3.

Quantum Field Theory Simulations

9.2.4.

Condensed Matter Physics

9.2.4.1.

Many-Body Systems

9.2.4.2.

Quantum Phase Transitions

9.2.4.3.

Strongly Correlated Systems

9.3.

9.3.1.

Combinatorial Optimization Problems

9.3.1.1.

Traveling Salesman Problem

9.3.1.2.

Maximum Cut Problem

9.3.1.3.

9.3.2.

Solving NP-Hard Problems

9.3.2.1.

Mapping to Quantum Algorithms

9.3.2.2.

Quantum Annealing Approaches

9.3.3.

Logistics and Scheduling

9.3.3.1.

Route Optimization

9.3.3.2.

Resource Allocation

9.3.3.3.

Supply Chain Management

9.3.4.

Financial Modeling

9.3.4.1.

Portfolio Optimization

9.3.4.2.

9.3.4.3.

9.3.4.4.

Monte Carlo Methods

9.4.

Machine Learning and AI

9.4.1.

Quantum Machine Learning

9.4.1.1.

Quantum Feature Maps

9.4.1.2.

Quantum Kernels

9.4.1.3.

Quantum Neural Networks

9.4.2.

Pattern Recognition

9.4.3.

Data Analysis and Classification

9.4.4.

Quantum-Enhanced Optimization for ML

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10. Quantum Software and Programming