Quantum Computing
From qubits to quantum algorithms — understanding the technology built on the foundations of quantum mechanical principles.
Bloch Sphere — Qubit State Representation
Quantum Entanglement — Correlated States
Qubits
The fundamental unit of quantum information. Unlike classical bits that exist as 0 or 1, qubits exploit superposition to exist in both states simultaneously. This exponential state space is the source of quantum computing's power.
- Classical bits vs quantum bits
- Superposition and the Bloch sphere representation
- Physical implementations: superconducting, trapped ion, photonic
- Decoherence and the fragility of quantum states
Quantum Gates
Quantum gates are the building blocks of quantum circuits. They manipulate qubits through unitary transformations, enabling operations impossible in classical computing — such as creating entanglement and exploiting interference.
- Single-qubit gates: Hadamard, Pauli-X/Y/Z, Phase
- Multi-qubit gates: CNOT, Toffoli, SWAP
- Universal gate sets and quantum circuit models
- Reversibility and unitarity constraints
Algorithms
Quantum algorithms exploit quantum mechanical properties to achieve computational speedups over classical approaches. From factoring large integers to searching unsorted databases, these algorithms define the frontier of computational theory.
- Shor's algorithm: polynomial-time integer factorization
- Grover's search: quadratic speedup for unstructured search
- Variational Quantum Eigensolver (VQE)
- Quantum approximate optimization (QAOA)
Cryptography
Quantum cryptography leverages the laws of physics — not computational hardness — to guarantee security. Quantum key distribution makes eavesdropping physically detectable, while quantum computing threatens classical encryption schemes.
- Quantum key distribution (BB84 protocol)
- No-cloning theorem as security foundation
- Post-quantum cryptography and lattice-based schemes
- Threat to RSA and elliptic curve cryptography