Quantum Computing

From Moore's Law limits to quantum advantage — why quantum computers work fundamentally differently from classical machines.

Complex numbers, vectors, matrices, tensor products, and Dirac notation — the mathematical toolkit every quantum programmer needs.

Superposition, the Bloch sphere, Born Rule, quantum phase, and what measuring a qubit actually means mathematically.

Pauli gates, Hadamard, phase gates, rotation gates, and how unitary matrices implement reversible quantum operations.

Circuit notation, multi-qubit systems, Bell states, entanglement, teleportation, and how noise limits circuit depth.

Deutsch, Grover, Shor, QFT, and variational algorithms — the algorithmic primitives that deliver quantum speedups.

Qiskit, Cirq, and PennyLane — building, simulating, and running circuits on real quantum hardware in the cloud.

Superconducting qubits, trapped ions, photonics, neutral atoms, decoherence, and what makes quantum hardware so hard to build.

Surface codes, fault tolerance, the threshold theorem, error mitigation, and the road to scalable quantum computation.

Quantum ML, quantum chemistry, QKD, post-quantum cryptography, and the open problems shaping the next decade of research.