Quantum Computing : A Comprehensive Beginner's Guide

Learn quantum computing fundamentals: qubits in superposition of zero and one, using ket and bra notation with alpha and beta as complex amplitudes and square-magnitude probabilities.

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.

Explore matrix representations of multi-qubit states, compute bras and inner products (brackets) for gates using bra-ket notation, and verify normalization with an equal-amplitude qubit example.

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.

The X gate, the quantum counterpart of the classic not gate, is reversible and swaps |0> and |1> using the 2x2 matrix [0 1; 1 0].

Apply the X gate to a general qubit alpha|0> + beta|1>, yielding alpha|1> + beta|0>. The X gate maps X|0> to |1> and X|1> to |0>, as described.

Explore the X gate acting on a qubit, yielding 1/√2 X0 + 1/√2 X1 in matrix form. Compare coefficients for different states and anticipate the hadamard gate.

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.

Explores multiple qubits, presents the four computational basis states for two qubits, and derives their matrix representations as tensor products of the ket zero and ket one.

Explore the cnot gate, a two-qubit gate, via its matrix representation and gate notation, showing how a control qubit flips the target when the control is one.

apply an x gate to the first qubit, apply a cnot with the first qubit as control, then apply a second x gate to produce the state |01> from |00>.

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.

Learn how to apply an X gate to the first qubit in a quantum circuit, simulate with Qiskit's state vector backend, and inspect the resulting state vector.

Demonstrate the hadamard gate by building a small quantum circuit, compute the state vector with a state vector simulator, and confirm a superposition of zero and one.

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.

Create a two-qubit quantum circuit in Qiskit, apply a CNOT gate with the first qubit as control and the second as target, then measure and plot the histogram.

Explore CNOT gate behavior with an X gate applied to the first qubit, add a barrier, and predict outcomes by plotting a histogram of counts from a quantum circuit.

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.