Quantum Computing and Quantum Machine Learning - Part 1

Learn the postulates of quantum mechanics formed from key assumptions used to explain phenomena and solve problems in quantum computing and quantum machine learning.

Compare classical state prediction with position and momentum to quantum mechanics' state vector psi in Hilbert space, formed from real numbers and unit vectors like i, j, k.

Explore the fundamentals of complex numbers, including the imaginary unit i, real and imaginary parts, and operations such as addition, subtraction, multiplication, and division, conjugates, Argand plane, and polar representation.

Explore how matrices power artificial intelligence, deep learning, and computer vision, how they solve simple linear equations, and see a pens and pencils example in matrix notation with the transpose.

Master matrix multiplication by traversing matrix a left-to-right and matrix b top-to-bottom, using the thumb rule that left's columns equal right's rows to compute the result.

Explore differentiation as the rate of change and slope, using rise over run, relate to Young's modulus, and apply differential equations to model disease spread, weather, traffic, and population growth.

Explore the distinction between scalars and vectors, learn how to compute vector magnitude and unit vectors, and understand initial and terminal points with practical examples.

Contrast classical and quantum mechanics: deterministic football motion versus quantum waves that interfere constructively or destructively. Learn about group velocity and phase velocity with rugby haka as an analogy.

Explore the Schrödinger equation and its link to quantum wave packets. Learn how monochromatic, undamped waves relate to the wave function psi and the classic wave equation.

Explain how Euler's formula links two wave equations, showing the imaginary term does not affect the output, and present the Schrodinger equation as a Hamiltonian with kinetic and potential energy.

Explore normalization of the wave function, using psi to derive probability density across an ensemble of identical quantum states and understand position distribution.

Explore how wave function probability equals psi times psi conjugate, and how normalization by root n preserves probability, introducing ortho normality and unit vectors via psi1 and psi2.

Apply Dirac notations to polarized light, using ket and bra vectors, inner products. Normalize diagonal states and compute transmission probabilities through polarizers, illustrating 0%, 50%, 100%.

Reflect on the journey through foundational quantum mechanics, Dirac notation, and the probabilistic nature of quantum particles, and preview part two on programming a quantum computer.