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Advanced Β· 12 Topics
Quantum Information & Computing
Qubits, quantum gates, entanglement, quantum algorithms, error correction, and the theory of quantum computation.
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Qubits & Quantum States
The quantum bit β superposition, measurement, and the Bloch sphere.
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Quantum Gates & Circuits
Unitary operations on qubits β the Pauli gates, Hadamard, CNOT, and circuit universality.
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Quantum Entanglement
Non-separable quantum states, Bell states, EPR, and the no-cloning theorem.
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Quantum Teleportation
Transmitting a qubit state using entanglement and two classical bits.
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Quantum Fourier Transform
Exponentially efficient Fourier transform β the engine of Shor's algorithm.
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Deutsch-Jozsa & Bernstein-Vazirani
The first quantum algorithms proving exponential speedup over classical computation.
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Grover's Search Algorithm
Quadratic quantum speedup for unstructured database search.
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Shor's Factoring Algorithm
Polynomial-time quantum factoring β and the threat to RSA cryptography.
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Quantum Error Correction
Protecting quantum information from decoherence using redundancy without measuring the state.
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Quantum Cryptography & BB84
Information-theoretically secure key distribution using quantum mechanics.
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Density Matrices & Open Systems
Mixed states, decoherence, von Neumann entropy, and open quantum systems.
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Quantum Complexity Theory
BQP, quantum advantage, and the frontier of what quantum computers can solve faster.
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