Quantum Computing

Quantum Computing • Unit 4

The core of quantum computation. Build from qubits and superposition through quantum circuits to powerful algorithms like Deutsch's algorithm and quantum teleportation.

Core Concepts

Qubits and superposition – quantum bits that exist in multiple states simultaneously
Measurement and Born's rule – how observation collapses quantum states probabilistically
Unitary evolution – quantum operations preserve probability and are reversible
Dirac notation – bra-ket notation for elegant quantum calculations
Pauli matrices – the fundamental single-qubit gates X, Y, Z and phase operations
Multi-qubit systems – tensor products and entanglement
Quantum circuits – composing gates to build algorithms
Deutsch's algorithm – quantum speedup through interference and phase kickback
Quantum teleportation – transmitting quantum states using entanglement and classical communication
No-cloning theorem – why quantum information cannot be copied

$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$

$P(0) = |\alpha|^2, \; P(1) = |\beta|^2$

$|\psi'\rangle = U|\psi\rangle$

$|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$

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