Certificate Course
in
Classical and Quantum Computing
The course gives an introduction into
classical and quantum computing. The course can also be done
in self-study.
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Under Construction
Problems and Solutions in Scientific Computing (postscript format).
Problems and Solutions in Scientific Computing (pdf format).
Exercises
Classical Part
Exercise I
(ps)
(pdf) ---
Exercise I Solutions
(ps)
(pdf)
Exercise II
(ps)
(pdf) ---
Exercise II Solutions
(ps)
(pdf)
Exercise III
(ps)
(pdf) ---
Exercise III Solutions
(ps)
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Exercise IV
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(pdf) ---
Exercise IV Solutions
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Exercise V
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Exercise V Solutions
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Exercise VI
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(pdf) ---
Exercise VI Solutions
(ps)
(pdf)
Exercise VII
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Exercise VII Solutions
(ps)
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Exercise VIII
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Exercise VIII Solutions
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Exercise IX
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Exercise IX Solutions
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Exercise X
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Exercise X Solutions
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Exercise XI
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Exercise XI Solutions
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Exercise XII
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Exercise XII Solutions
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Exercise XIII
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Exercise XIII Solutions
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Exercise XIV
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Exercise XIV Solutions
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Exercise XV
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Exercise XV Solutions
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Exercise XVI
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Exercise XVI Solutions
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Exercise XVII
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Exercise XVII Solutions
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Exercise XVIII
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Exercise XVIII Solutions
(ps)
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Exercise XIX
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Exercise XIX Solutions
(ps)
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Quantum Part
Exercise I
(ps)
(pdf) ---
Exercise I Solutions
(ps)
(pdf)
Exercise II
(ps)
(pdf) ---
Exercise II Solutions
(ps)
(pdf)
Exercise III
(ps)
(pdf) ---
Exercise III Solutions
(ps)
(pdf)
Exercise IV
(ps)
(pdf) ---
Exercise IV Solutions
(ps)
(pdf)
Exercise V
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(pdf) ---
Exercise V Solutions
(ps)
(pdf)
Exercise VI
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(pdf) ---
Exercise VI Solutions
(ps)
(pdf)
Exercise VII
(ps)
(pdf) ---
Exercise VII Solutions
(ps)
(pdf)
Exercise VIII
(ps)
(pdf) ---
Exercise VIII Solutions
(ps)
(pdf)
Exercise IX
(ps)
(pdf) ---
Exercise IX Solutions
(ps)
(pdf)
Exercise X
(ps)
(pdf) ---
Exercise X Solutions
(ps)
(pdf)
Exercise XI
(ps)
(pdf) ---
Exercise XI Solutions
(ps)
(pdf)
Exercise XII
(ps)
(pdf) ---
Exercise XII Solutions
(ps)
(pdf)
Table of Contents
Part I - Classical Computing
Algorithms
- Algorithms
- Algorithm Verification
- Random Algorithms
- Total and Partial Functions
- Alphabets and Words
Boolean Algebra
- Introduction
- Definitions
- Rules and Laws of Boolean Algebra
- DeMorgan's Theorem
- Further Definitions
- Boolean Function Implementation
- Karnaugh Maps
- Quine-McKluskey Method
- Example Programs
- Efficient Set Operations Using Boolean Algebra
- Quine-McKluskey Implementation
Number Representation
- Binary, Decimal and Hexadecimal Numbers
- Conversion
- Arithmetic
- Signed Integers
- Sign and Magnitude
- One's Complement
- Two's Complement
- Overflow
- Binary-Coded Decimal Form
- Floating Point Instruction
- Introduction
- Representation
Logic Gates
- Introduction
- Gates
- AND Gate
- OR Gate
- XOR Gate
- NOT Gate (Inverter)
- NAND Gate
- NOR Gate
- XNOR Gate
- Buffer
- Tri-State Logic
- Feedback and Gates
Combinational Circuits
- Introduction
- Decoder
- Encoder
- Demultiplexer
- Multiplexer
- Binary Adder
- Binary Half Adder
- Binary Full Adder
- Binary Four-Bit Adder
- Faster Addition
- Binary Subtraction
- Binary Multiplication
- Unsigned Integer Multiplication
- Fast Multiplication
- Signed Integer Multiplication
- Binary Division
- Magnitude Comparator
- 4-Bit ALU
- Read Only Memory (ROM)
- Combinational Programmable Logic Devices
- Programmable Gate Arrays
- VHDL
Latches and Registers
- Introduction
- SR Latch
- D Latch
- JK Latch
- D Register
- JK Register
Synchronous Circuits
- Introduction
- Shift Registers
- Binary Counter
- Example Programs
Recursion
- Introduction
- Example Programs
- Mutual Recursion
- Wavelets and Recursion
- Primitive Recursive Functions
- Backtracking
- Stacks and Recursion Mechanisms
- Recursion Using Stacks
- Stack Free Recursion
Abstract Data Type
- Introduction
- Linked List
- Stack
- Tree
Error Detection and Correction
- Introduction
- Parity Function
- Hamming Codes
- Weighted Checksum
- Noiseless Coding Theorem
- Example Programs
Cryptography
- Introduction
- Classical Cypher Systems
- Public Key Cryptography
Finite State Machines
- Introduction
- Finite Automata
- Finite Automata with Output
- Turing Machines
- Example Programs
Computability and Complexity
- Introduction
- Computability
- Church's Thesis
- The Halting Problem
- Gödel's Incompleteness Theorem
- Gödel Numbering
- Gödel's Incompleteness Theorem
- Complexity
- Complexity of Bit Strings
- NP-class of Problems
Neural Networks
- Introduction
- Hyperplanes
- Perceptron
- Introduction
- Boolean Functions
- Perceptron Learning
- Quadratic Threshold Gates
- One and Two Layered Networks
- Perceptron Learning Algorithm
- The XOR Problem and Two-Layered Networks
- Multilayer Perceptrons
- Introduction
- Cybenko's Theorem
- Back-Propagation Algorithm
Genetic Algorithms
- Introduction
- The Sequential Genetic Algorithm
- Gray Code
- Schemata Theorem
- Markov Chain Analysis
- Bit Set Classes in C++ and Java
- Bitwise Operations
- A Bit Vector Class
- Maximum of One-Dimensional Maps
- Maximum of Two-Dimensional Maps
- The Four Colour Problem
- Problems with Constraints
- Introduction
- Knapsack Problem
- Traveling Salesman Problem
- Other Applications for Genetic Algorithms
- Distributed Global Optimization
- Genetic Programming
Part II - Quantum Computing
Quantum Mechanics
- Hilbert Spaces
- Schmidt Decomposition
- Linear Operators in Hilbert Spaces
- Unitary Operators
- Spin Matrices and Kronecker Product
- Postulates of Quantum Mechanics
Quantum Bits and Quantum Computation
- Introduction
- Quantum Bits and Quantum Registers
- Quantum Bit
- Quantum Registers
- Entangled States
- Quantum Gates
- NOT Gate
- Walsh-Hadamard Gate
- XOR and Controlled NOT Gate
- Other Quantum Gates
- Universal Sets of Quantum Gates
- Functions
- Garbage Disposal
- Quantum Copying
- Example Programs
Measurement and Quantum States
- Introduction
- Measurement Problem
- Copenhagen Interpretation
- Hidden Variable Theories
- Everett Interpretation
- Basis Degeneracy Problem
- Information Theoretic Viewpoint
Quantum State Machines
- Introduction
- Quantum Automata
- Quantum Turing Machines
Teleportation
- Introduction
- Teleportation Algorithm
- Example Program
Quantum Algorithms
- Deutch's Problem
- Quantum Key Distribution
- Dense Coding
- Quantum Fourier Transform
- Factoring (Shor's Algorithm)
- Unstructured Search (Grover's Algorithm)
Quantum Information Theory
- Introduction
- Von Neumann Entropy
- Measure of Entanglement
- Bell's Inequality
- Entanglement of Formation
- Conditions on Entanglement Measures
- Quantum Coding
- Holevo Bound
Quantum Error Detection and Correction
- Introduction
- The Nine-qubit Code
- The Seven-qubit Code
- Efficiency and the Five-qubit Code
- Stabilizer Codes
Quantum Hardware
- Introduction
- Trapped Ions
- Cavity Quantum Electrodynamics
- Quantum Dots
- Nuclear Magnetic Resonance Spectroscopy
Access the source code
Timetable and Enrollment Forms.
Literature to Quantum Computing
of the
International School for Scientific Computing
1) Classical and Quantum Computing
by
Yorick Hardy and Willi-Hans Steeb
Birkhäuser Publishing, Basel, 2001
ISBN 3-7643-6610-9
2) Hilbert Spaces, Wavelets, Generalized Functions and
Modern Quantum Mechanics
by
Willi-Hans Steeb
Kluwer Academic Publisher, Dordrecht, 1998
ISBN 0-7923-5231-9
3) Matrix Calculus and Kronecker Product with
Applications and C++ Programs
by
Willi-Hans Steeb
World Scientific, Singapore, 1997
ISBN 981-02-3241-1
Publications
1) Entangled Quantum States and a C++ Implementation
Willi-Hans Steeb and Yorick Hardy
International Journal of Modern Physics C, Vol. 11, 2000
2) Quantum Computing and SymbolicC++ Simulations
Willi-Hans Steeb and Yorick Hardy
International Journal of Modern Physics C, Vol. 11, 2000
3) Entangled Quantum States
Willi-Hans Steeb and Yorick Hardy
International Journal of Theoretical Physics, Vol. 39, 2000
4) Energy Eigenvalue Level Motion and a SymbolicC++ Implementation
Willi-Hans Steeb and Yorick Hardy
International Journal of Modern Physics C, Vol. 11, 2000
Source code from the publications
Other research projects:
Level Repulsion and Entangled States
Hubbard Model and Quantum Computing
Mixed States and Entanglement
For further information please contact Prof. Willi-Hans Steeb
E-mail1: whsteeb AT uj DOT ac DOT za
E-mail2: steeb_wh@yahoo.com
or Yorick Hardy
E-mail: yorickhardy@yahoo.com