Quantum 101

Table of Contents Introduction Classical vs Quantum Approach Problem Statement Overview of the Deutsch Algorithm Mathematical Formulation Oracle Function Quantum Circuit Design Initial State Preparation Applying Hadamard Gates Oracle Application in Superposition Final Hadamard on...

Table of Contents Introduction What Is a Quantum Circuit? Components of a Quantum Circuit Qubits as Wires Gates as Operations on Wires Time Flow and Diagram Layout Single-Qubit Gate Symbols Multi-Qubit Gate...

Table of Contents Introduction What Is the Bloch Sphere? State of a Qubit Parametrization of Qubit States General Form of a Single-Qubit Pure State Normalization and Global Phase Coordinate Mapping on...

Table of Contents Introduction What Are Universal Gate Sets? Classical Logic Universality vs Quantum Universality Unitary Operations and Quantum Logic Criteria for Universality The Solovay-Kitaev Theorem Single-Qubit and Two-Qubit Gates Universality with...

Table of Contents Introduction Basics of Controlled Gates The Concept of Control and Target Qubits Controlled Gates as Conditional Operations Matrix Representation of CNOT Action of CNOT on Basis States Creating...

Table of Contents Introduction Phase and T Gates in Quantum Circuits Importance of Phase in Quantum Computation Matrix Representations The Phase (S) Gate The T Gate (π/8 Gate) Action on Computational...

Table of Contents Introduction Quantum Gates as Unitary Operators The Pauli Gates: X, Y, Z Matrix Representations The X Gate (Bit-Flip) The Y Gate (Bit and Phase Flip) The Z Gate...

Table of Contents Introduction Classical vs Quantum Measurement The Postulates of Quantum Measurement Measurement in Dirac Notation Projective Measurements Measurement Basis and Observable Operators Measurement Probabilities and the Born Rule Collapse of...

Table of Contents Introduction Qubits and Composite Systems What is a Tensor Product? Mathematical Definition Tensor Product of Two Qubits Notation and Dimensionality Multi-Qubit Basis States Example: Tensoring |0⟩ and |1⟩ Associativity of...

Table of Contents Introduction The Quantum Nature of Information Classical vs Quantum Parallelism Understanding Superposition Dirac Notation for Superposition The Role of the Bloch Sphere Visualizing Superposed States Constructing Superpositions with Quantum...

Table of Contents Introduction Classical Bits vs Quantum Bits The Concept of a Qubit Dirac Notation and Qubit States The Bloch Sphere Representation Hilbert Space: Definition and Structure Inner Product and...

Table of Contents Introduction Overview of Classical Computation Information Representation in Classical Systems Logic Gates and Classical Circuits Turing Machines and Classical Universality Limitations of Classical Computation Introduction to Quantum Computation Qubits...