Quantum Computing: Fundamentals and Frontiers

Quantum Computing: Fundamentals and Frontiers

1. Core Principles

Qubit (Quantum Bit)

• Superposition: Unlike classical bits (0 or 1), qubits exist in states �∣0⟩+�∣1⟩α∣0⟩+β∣1⟩, where ∣�∣2+∣�∣2=1∣α∣2+∣β∣2=1.

• Entanglement: Qubits can be correlated such that the state of one instantly influences another (Einstein's "spooky action at a distance").

Quantum Gates

• Hadamard Gate (H): Creates superposition ∣0⟩→∣0⟩+∣1⟩2∣0⟩→2​∣0⟩+∣1⟩​.

• CNOT Gate: Entangles two qubits (basis for quantum circuits).

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2. Quantum Algorithms

Algorithm	Speedup