TEKNISKA HOGSKOLAN I LINKOPING
Institut for fysik och matteknik
Iryna Yakymenko
tel.: 288947
e-mail:irina@ifm.liu.se
02.01.2009

QUANTUM COMPUTERS, TFYA19, 6 ECTS points


Library page

The course represents a comprehensive survey on the concept of quantum computing with an exposition of qubits, quantum logic gates, quantum algorithms and their implementation. Starting with the main definitions of the theory of computation, the course will mostly deal 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 will also be considered.

The course includes the basic physics and computer science information necessary to understand the idea of quantum computing and its applications, i.e. the elements of the theory of sets, mathematical logic, probability theory, theory of computation, quantum mechanics, thermodynamic and statistical physics, semiconductor physics and nanotechnology.

The course has a cross-disciplinary nature and can be equally useful for physicists of different profiles, computer scientists and engineering students.

The course is giving in a spring semester by Irina Yakimenko, period 2 (vt2) and contains 20 lectures. Course language is English.

Course Literature

  1. M.A. Nielsen, I.L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
  2. I.I. Yakimenko. Lecture Notes in Quantum Computers, 2009.

  3. plus selected articles plus some chapters from:
    1. R.P. Feynman. Feynman Lectures on Computation, Addison-Wesley, 1996.
    2. G.J.Milburn. The Feynman Processor. Helix Books, Reading, Massachusetts, 1998.
    3. C.P. Williams, S.H. Clearwater. Explorations in Quantum Computing, Springer, 1998.
    4. G.P. Berman, G.D. Doolen, R. Mainieri, V.I. Tsifrinovich. Introduction to Quantum Computers, World Scientific Publishing, 1998.
    5. G. Benenti, G. Casati, G. Strini.Principles of Quantum Computation and Quantum Information, Vol. I, World Scientific, 2004.

    Examination

    Solution of the home problems, numerical projects and oral examination.

    Course Organization

    Lecture 1: COMPUTER ORGANIZATION

    Introduction. Binary System. Boolean Algebra. "Practical" Computer for Addition. Logic Gates.

    Lecture 2-3: THEORY OF COMPUTATION

    More about Logic Gates: Reversible Gates. Algorithm: Nonformal Definition. Recursive Functions and Effective Computability.

    Lecture 4: QUBITS

    From Bits to Qubits. Qubit: Abstract Definition. Multiple Qubits. Classical and Quantum Coin-Toss.

    Lecture 5: QUANTUM GATES

    Introduction. Transformations in Qubit Systems. Singlr Qubit Gates. Square-of-Not Gate.

    Lecture 6: QUANTUM CIRCUITS

    Simple Quantum Circuits. No-Cloning Theorem. Quantum Teleportation. Simulation of Quantum Systems.

    Lecture 7: QUANTUM ALGORITHMS

    Introduction. Quantum Parallelism. Deutsch's Algorithm. Deutsch-Jozsa Algorithm and Deutsch Problem. Period-Finding Algorithm.

    Lecture 8-9: SPIN IMPLEMENTATION OF QUANTUM GATES

    Schrodinger Equation for Proton Spin in Magnetic Field. Spin Precession. Spin in Resonant Magnetic Field. N- and H-Gate Implementation. Spin in Resonant Magnetic Field with Phase Shift.

    Lecture 10: SPIN DYNAMICS AT FINITE TEMPERATURE

    Quantum Systems at Zero and Finite Temperatures. Nuclear Spins at Finite Temperature. Ensemble of Nuclear Spins in Resonant Electromagnetic Field. Spin Dynamics in Heisenberg Representation.

    Lecture 11-12: INTERACTING SPINS

    Two-Spin Interaction. Dynamical Behaviour of Two-Spin Based Quantum CN-Gate. Linear Chains of Nuclear Spins. Digital Gates in Spin Chains.

    Lecture 13-14:PHYSICAL REALISATION OF QUANTUM COMPUTATION
    Basic Requirements for Quantum Computation. Ion Trap-Based Quantum Computer. QED-Based Quantum Computer. NMR-Based Quantum Computer. Solid-State Quantum Computer.

    Lecture 15: QUANTUM FOURIER TRANSFORM AND PHASE ESTIMATION

    Quantum Fourier Transform. Quantum Circuit for Quantum Fourier Transform. Quantum Phase Estimation.

    Lecture 16-17: ORDER-FINDING AND FACTORING

    Introduction. Modular arithmetic. Order-Finding. Factoring. Discrete Logarithms.

    Lecture 18: QUANTUM SEARCH ALGORITHMS

    Search Problem. Procedure of Quantum Search Algorithms. Geometrical Visualisation. Quantum Countimg.

    Lecture 19: QUANTUM ALGORITHM FOR EIGENVALUE ESTIMATION

    Lecture 20: QUANTUM CRYPTOGRAPHY

    What is wrong with classical cryptography? RSA Public-Key Cryptography. Quantum cryptography.Quantum Error Correction.