
Trace the origins of quantum theory from Planck's quanta and blackbody radiation to quantum mechanics, highlighting Einstein and Bohr, photons, wave mechanics, and the Schrödinger equation.
Master the Pauli matrices—sigma one, sigma two, sigma three—as two-by-two hermitian operators with zero trace and eigenvalues ±1, describing spin along x, y, z and their multiplication rules.
Explore unitary transformations generated by Pauli matrices to manipulate qubits while preserving their probability amplitudes, and see how the identity generator yields global phase and builds universal gates.
Show how unitary evolution of density matrix yields a z-rotation by theta, expanded via Pauli matrices to cosine theta times x plus sine theta times y on the Bloch sphere.
Apply the ry gate to rotate a qubit around the y axis by theta, creating superposition and phase changes in |0⟩ and |1⟩.
The tensor product merges multiple qubits into a larger quantum system, enabling superposition and multi-qubit computation. It preserves properties like associativity, distributivity, and scalar factoring, and underpins quantum circuits.
Explore the Fredkin gate, a three-qubit controlled swap that swaps the second and third qubits when the control is 1 and leaves them unchanged when the control is 0.
Explore linear evolution under Schrödinger equation and collapse upon measurement to eigenstates with projective measurements, yielding classical bits with probabilities equal to the squares of alpha and beta.
Derive the completeness equation from an orthonormal basis by summing outer products to obtain the identity, showing any vector spans the space.
Explore projection measurements that project a quantum state onto eigenstates of an observable, yielding outcomes with eigenvalues and probabilities via the state's collapse.
Explore how a quantum circuit uses measurement operators m0 and m1 to project a single qubit onto |0> or |1>, with probabilities derived from its state.
Explore how initial state preparation builds target superpositions from the ground state using gates, distinguish pure and mixed states, and harness entanglement for quantum computing.
Use the hadamard test to estimate the real part of a quantum state's amplitude relative to a reference, via a controlled unitary and a final hadamard measurement.
This comprehensive course is suitable for a wide range of learners, from those who are just beginning to explore quantum computing to experts in the field. Our aim is to cover every aspect of quantum computing, starting from the basics and progressing to complex application scenarios. Unlike other courses, we place a strong emphasis on learning quantum computing through linear algebra and provide detailed matrices and vector calculations for key concepts, allowing you to develop a solid understanding of the subject matter.
The course is divided into two main parts, each of which is designed to provide learners with a deep understanding of quantum computing:
Basic part, which includes:
An overview of quantum computing, quantum bits, single quantum bit logical gates, multi-quantum bit logical gates, quantum measurement, quantum circuits, and more.
Algorithm part, which includes:
The Hadamard Test, SWAP Test, amplitude amplification, quantum Fourier transform, quantum phase estimation, quantum arithmetic, the HHL algorithm, Deutsch-Josza algorithm, Grover algorithm, and more.
But that's not all - we're continually updating and improving the course to include even more valuable information, such as:
Programming part, which includes:
Examples of basic logic gates based on Qiskit, as well as learning examples of algorithms.
Machine learning part, which includes:
Algorithms and implementations of quantum machine learning and quantum artificial intelligence.
Application part, which includes:
The application of quantum computing technology in finance and other fields, allowing you to gain a broader understanding of how quantum computing is transforming industries and changing the face of technology.