Quantum Computing : A Comprehensive Beginner's Guide

Calculate probabilities for measuring state zero and state one using ket notation, amplitudes like 1/√2, and complex conjugates; verify normalization via bra-ket inner products.

Learn the Bloch sphere, named after Felix Bloch, to map a qubit. The north pole is |0>, the south pole is |1>, with plus and minus states on the surface.

Explore the Hadamard gate, its matrix form, and how it maps |0> to (|0>+|1>)/√2 and |1> to (|0>-|1>)/√2, creating superposition.

The z gate performs a phase flip: z|0> = |0>, z|1> = -|1>, and it maps |+> to |-> and |-> to |+> with a pi phase shift.

Explore the S gate, its matrix representation, and how it leaves |0> unchanged while mapping |1> to i|1>, transforming a general qubit alpha|0>+beta|1> into alpha|0>+i beta|1>.

Explore how single and multiple qubits combine via tensor products, using column vectors and explicit calculations to yield four- and sixteen-element results.

Explore creating the first Bell state phi plus using a Hadamard gate and a CNOT gate to illustrate superposition and entanglement of two qubits.

Learn to build a basic quantum circuit in Qiskit by creating a one-qubit register and a one-bit classical register, adding measurement, drawing with Matplotlib, and applying an X gate.

Demonstrates measuring a quantum state and observing state vector changes after a Hadamard gate, with measurement in the sr register and result storage in the cr register, plus circuit drawing.

Plot the Bloch sphere from a state vector using qiskit visualization, then measure the qubit and plot a histogram to compare theoretical 0.5 probabilities with simulated counts.

Set up a two-qubit quantum register and circuit with a CNOT gate, print the state vector, and plot the Bloch sphere using the qiskit state vector simulator and visualization tools.

Explore the swap gate on a two-qubit system by building a circuit, applying an X gate, and visualizing before and after states on the Bloch sphere.

Learn how quantum entanglement forms the phi plus Bell state by starting from zero zero, applying a Hadamard gate to the first qubit, then a C-not gate.

Learn superdense coding with Qiskit by building entangled states using Hadamard and CNOT gates, then transmit and measure messages with histograms and a Qiskit simulator.