Quantum Computing and Quantum Machine Learning - Part 2

Explore how superposition combines states, illustrated by light polarization through parallel and perpendicular polarizers, where alignment controls light transmission and extinction.

Contrast a classical bit (0 or 1) with a qubit that exists everywhere until measured under the superposition principle. See how measurement collapses and disturbs the quantum state.

Apply the superposition principle to model an electron’s state as a weighted sum of basis states with complex amplitudes alpha_0, alpha_1, alpha_2, yielding probabilities |alpha_i|^2 that normalize to one.

Explore the geometrical interpretation of quantum states through the superposition principle, using complex probability amplitudes, normalization of state vectors, and column-vector representations for two- and three-level systems to compute probabilities.

Measure quantum states in arbitrary bases and derive probabilities from amplitudes. See how measurement collapses the state and how basis choice, including plus and minus bases, affects outcomes.

Explore how a two-qubit system forms a superposition of all four basis states, with amplitudes α00, α01, α10, α11, normalized to one. The lecture illustrates measurement collapsing states and probabilities.

Explore entanglement as a key quantum phenomenon, form composite two-qubit states, examine factorization versus entangled states, and study Bell states and measurement outcomes.

Investigate quantum gates and their unitary matrix representations. Examine the quantum not gate, which flips basis states and preserves state length, using the matrix [[0,1],[1,0]].

Explore the Pauli X gate, its unitary matrix [[0,1],[1,0]], and how it reverses basis states; compare with xor behavior on arbitrary quantum states.

Explain the Pauli z gate, a phase flip gate, represented by the diag(1,-1) matrix. Applying it to the state alpha zero plus beta one yields alpha zero minus beta one.

Discover how the Bloch sphere visualizes a qubit from the state alpha|0>+beta|1>, with complex alpha and beta, mapped to dimensions by latitude and longitude. Global phase does not affect observables.

Represent the qubit state on the Bloch sphere by expressing α and β in terms of θ and φ, ensuring |α|^2+|β|^2=1.

Learn how multi-particle systems arise from tensor products of single-particle Hilbert space bases to form a composite Hilbert space, and how to compute tensor products of states with coefficients.

Set up an IBM quantum experience account, verify via email, accept the end user agreement, then explore circuit composer and install the casket library to run Jupiter notebook.

Set up a Jupyter notebook with Qiskit and IBM Quantum Experience, verify installation, and configure your API token. Run a five-qubit qasm simulator to visualize measurement probabilities.

Open a Jupiter notebook to experiment with cubits, visualize states in plus minus and clockwise anticlockwise bases, and derive probabilities from probability amplitudes on the block sphere.

Conclude part two by revisiting superposition and entanglement, gates like Hadamard and Pauli X, Y and Z, eigenvalues and eigenvectors, Bloch sphere visualization, and programming with IBM Quantum Experience Lab.