Quantum Computers

Aim

The course represents a comprehensive survey on the concept of quantum computing with an exposition of qubits, quantum logic gates, quantum algorithms and implementation. Starting with the main definitions of the theory of computation, the course mostly deals with the application of the laws of quantum mechanics to quantum computing and quantum algorithms. Some related topics concerned mainly to the problem of quantum communication are also be considered. To achieve this aim students should be able to

• know the definition of qubit, quantum logic gates, quantum circuits and quantum algorithms
• understand how quantum parallelism is used in the simplest quantum algorithms such as Deutsch, period finding and quantum Fourier transform

Content

Computer organization and theory of computation: binary system, Boolean algebra, logic gates, quantum logic gates, algorithms, Turing machines and effective computability. Quantum mechanics and computers: from bits to qubits, superposition, measurement, classical and quantum coin-tosses, uncertainty principle. Quantum algorithms: quantum parallelism, discrete Fourier transfom, phase estimation, Shor's factoring and Grover's searching algorithms. Physical realization of quantum computation: ion trap, cavity QED, nuclear magnetic resonance (NMR) and solid-state-based quantum computers. Quantum cryptography, quantum teleportation and quantum error correction.

The course is cross-disciplinary and can be equally useful for engineering students in physics, computer science and electrical engineering.