Quantum Computing freeCodeCamp

• What principles does Quantum Computing leverage?

  Principles of quantum mechanics
• What are the two sections of the course focused on?

  Mathematics and mechanics of quantum computers
• Why are quantum computers considered powerful?

  They process information at incredible speeds
• Who created this Quantum Computing course?

  Michael from Quantum Sore
• What analogy is often used to explain quantum computers?

  Q bits that are both zero and one
• What was the purpose of creating this course?

  To provide a solid foundation without analogies
• What is the structure of the course?

  1. Basic mathematics for understanding
  2. Exploration of qubits and their representation
  3. Representation and operations on multiple qubits
  4. Analysis of quantum algorithms
• What basic mathematics is covered in the first section?

  Complex numbers and basic linear algebra
• What is a qubit?

  A quantum bit that can be zero and one
• What operations are explored in relation to qubits?

  Single qubit operations and their properties
• What strange quantum phenomena are discussed?

  Quantum entanglement and phase kickback
• What are the properties and operations of matrices in Quantum Computing?

  • 2D arrangement of numbers
  • Addition and subtraction of matrices
  • Multiplication by a scalar
  • Matrix multiplication rules
  • Identity matrix and its properties
  • Inverse of a matrix
  • Complex conjugate and transpose
• What is the definition of an M by N matrix?

  Matrix with M rows and N columns
• What is the identity matrix?

  All zeros except for ones on the diagonal
• What happens when you multiply a matrix by its inverse?

  You get the identity matrix
• What is a column vector?

  An n by 1 matrix
• What is the complex conjugate of a matrix?

  Flipping the sign of imaginary components
• What is the transpose of a matrix?

  Exchanging rows with columns
• What is a unitary matrix?

  Matrix where U * U dagger equals identity
• What is an eigenvector?

  Vector that stays in the same direction
• What is a qubit's representation in quantum computing?

  Column vectors 1 0 and 0 1
• What does superposition mean in quantum mechanics?

  Quantum particle is in two states simultaneously
• What happens when a qubit is measured?

  It collapses to either zero or one
• What do the numbers in a qubit's representation indicate?

  Probability of measuring zero or one
• What is the probability equation for measuring a qubit?

  Probability of zero + probability of one = 1
• What happens to a qubit in superposition when measured?

  It collapses into the measured state
• What are the key concepts of quantum measurement?

  • Changes the state of the system
  • Only measures zero or one
  • Probability based on amplitudes
  • Collapses superposition into a definite state
• What is the probability of measuring a one state?

  25%
• Why is the probability of measuring Z equal to 1?

  Because it is defined as the column vector 1 0
• What must the probabilities of measuring a zero and a one equal?

  They must equal one
• What happens when we measure a qbit in superposition?

  It collapses into the measured state
• What notation is used to represent quantum states mathematically?

  Dirac notation
• How do we convert a qbit state into Dirac notation?

  By factoring out the coefficients from matrices
• What do the brackets around the states in Dirac notation signify?

  They indicate quantum states
• What is the significance of the block sphere in quantum computing?

  • Represents quantum states graphically
  • Zero state at the top, one state at the bottom
  • States can be visualized as points on the sphere
  • Higher position indicates higher probability of measuring zero
• Where does the state $\frac{1}{\sqrt{2}}|0\rangle +$$\frac{1}{\sqrt{2}}|1\rangle$ lie on the block sphere?


  Halfway between the North and South Poles
• What does it mean for a qbit to spin around the sphere?

  It refers to the phase of the qbit
• What is the effect of applying the X gate to a qbit in the zero state?

  It flips the qbit to the one state
• What happens when the X gate is applied to a qbit halfway between 0 and 1?

  It flips the qbit 180° around the x-axis
• How does the Y gate differ from the X gate?

  It rotates the qbit 180° around the Y axis