Math Prerequisites for Quantum Computing A visual guide to the mathematics you need to master before you start learning quantum computing

Why Quantum Computing ? BOOLEAN ALGEBRA Working with True and False Boolean Variables and Operators Truth Tables Logic Gates Logic Circuits AND Gate OR Gate NOT Gate Multiple Input Gates Equivalent Circuits 1 Equivalent Circuits 2 Universal Gate NAND Exclusive-OR XOR for Assignment XOR of Bit Sequences 1 XOR of Bit Sequences 2 Introduction to Cryptography Cryptography with XOR Shared Secret Importance of Randomness Breaking the Code PROBABILITY Predicting the Future Probability of a Boolean Expression Mutually Exclusive Events Independent Events Manipulating Probabilities with Algebra P( Mutually Exclusive Events ) P( Independent Events ) Complete Set of MutEx Events P( A OR B ) Worked Examples 1 Worked Examples 2 P( Bit Values ) Analysis with Venn Diagrams Venn Diagram: P(A AND B) Venn Diagram: P( A OR B ) Venn Diagram: P( NOT A ) Worked Examples 1 Worked Examples 2 Conditional Probability Worked Examples STATISTICS Introduction to Statistics Random Variables Mapping Random Variables Mean, Average, Expected Value, ... Worked Examples 1 Worked Examples 2 Beyond Mean Standard Deviation Worked Examples Combinations of Random Variables Correlation Analysis of Correlation COMPLEX NUMBERS Introduction to Complex Numbers Imaginary i Addition of Complex Numbers Subtraction Multiplication by a Real Division by a Real Complex Multiplication Worked Examples Complex Conjugate Squared Magnitude Complex Division Worked Examples Euler's Formula Polar Form Worked Examples Fractional Powers Complex Cube Roots of 1 Square Root of i 2D Coordinates LINEAR ALGEBRA Introduction to Matrices Matrix Dimensions Matrix Addition Matrix Subtraction Scalar Multiplication Matrix Multiplication Worked Examples 1 Worked Examples 2 3x3 Example Worked Examples 1 Worked Examples 2 When is Multiplication Possible? Worked Examples Not Commutative Associative and Distributive Dimension of Result Odd Shaped Matrices Worked Examples 1 Worked Examples 2 Worked Examples 3 Inner Product Worked Examples Identity Matrix Matrix Inverse Transpose Worked Examples Transpose of Product Complex Conjugate of Matrices Adjoint Unitary Hermitian Hermitian and Unitary Why Hermitian or Unitary ? Vectors and Transformations Rotation in 2D Special Directions Eigen Vectors and Eigen Values More Eigen Vectors Dirac Bra-ket Notation QUBITS AND SUPERPOSITION From Bits to Qubits Polarized Photons of Light Photons and Polarizing Filters More on Photons and Polarizing Filters Filters Change Polarization Quantum Behavior of Polarizers Polarizing Single Photons Using Calcite Loss of Information Finding Angle of Polarization Finding Polarization of a Single Photon Limitations of Measurement Repeated Measurement 1 Repeated Measurement 2 Repeated Measurement with Filters Running the Java Code Simulation of Classical Bit Simulation of Qubit (Quantum Bit) No Cloning Theorem 1 No Cloning Theorem 2 Measurement is Irreversible Deterministic vs Probabilistic Simulating Measurements Superposition Collapse of Superposition Conclusion