Quantum Computing

  1. The Qubit: The Quantum Bit
    1. Definition of a Qubit
      1. Mathematical Definition
        1. Physical Realizations of Qubits
          1. Comparison to Classical Bits
          2. Representing Qubit States
            1. Basis States |0⟩ and |1⟩
              1. Computational Basis
                1. Physical Interpretation
                  1. Standard Basis Vectors
                  2. General Qubit State
                    1. Complex Coefficients
                      1. Normalization Condition
                        1. Global Phase
                        2. The Bloch Sphere Representation
                          1. Geometric Representation
                            1. Polar and Azimuthal Angles
                              1. Visualization of Pure States
                                1. Antipodal Points
                              2. Superposition
                                1. Linear Combinations of Basis States
                                  1. Superposition Principle
                                    1. Equal Superposition States
                                    2. Probability Amplitudes
                                      1. Squared Modulus and Measurement Probability
                                        1. Phase Information
                                      2. Measurement in the Computational Basis
                                        1. The Measurement Postulate
                                          1. Projective Measurement
                                            1. Measurement Operators
                                            2. Collapse of the Wave Function
                                              1. Post-Measurement State
                                                1. Irreversibility of Measurement
                                                2. Probabilistic Nature of Measurement
                                                  1. Born Rule
                                                    1. Repeated Measurements
                                                      1. Statistical Interpretation

                                                  Previous

                                                  1. Foundations of Quantum Computing

                                                  Go to top

                                                  Next

                                                  3. Multi-Qubit Systems