Essential Quantum Mechanics: vector space, basis and linear independence, linear operator and matrices, Pauli matrices, eigenvalues and eigenvectors, adjoint, Hermitian and unitary operators, state space, evolution of states, measurement, POVM measurements, phase, Bloch sphere, density operator, Schmidt decomposition, purification, EPR and Bell inequality; Quantum Circuits: quantum algorithms, single qubit operations, controlled operations, universal unitary gates; Quantum Fourier Transform: definition, phase estimation, order finding, factoring, period finding, discrete logarithms; Quantum Search Algorithm: oracle, the procedure, geometric visualization, performance, quantum search as quantum simulation, optimality of the search algorithm; Physical Realization of Quantum Computers: conditions for quantum computation, performance if unitary transformations, harmonic oscillator quantum computers, physical apparatus, Hamiltonian, quantum computation, optical photon quantum computer-physical apparatus, quantum computation, cavity quantum electrodynamics-physical apparatus, Hamiltonian, ion traps, nuclear magnetic resonance; Quantum Noise: classical noise and Markov process, environment and quantum operations, operator-sum representation, trace and partial trace, geometric picture of single qubit operation, quantum channels, phase damping; Quantum Error Correction: three qubit bit and phase flip code, the Shor code, discretization of errors, independent error model, degenerate codes, quantum Hamming bound, classical linear codes, Calderbank-Shor-Steane codes, stabilizer formalism, unitary gates and the stabilizer formalism, measurement in the stabilizer formalism, the Gottesman-Knill formalism, quantum circuits for encoding, decoding, and correction, fault-tolerant quantum computation; Entropy and Information: Shannon entropy, binary and relative entropy, conditional entropy and mutual information, Von Neumann entropy, basic properties, subadditivity, concavity of the entropy, strong subadditivity; Quantum Information Theory: the Holevo bound, example applications, data compression, Shannon’s noiseless channel coding theorem, classical information over noisy quantum channels, quantum information over noisy quantum channels, entanglement as a physical resource, quantum cryptography.