A quantum computer is the ultimate information processor in modern quantum technology, which uses quantum bits (qubits) and quantum circuits to perform computations. Large-scale quantum computers would be able to solve some problems much faster than their classical  counterparts that use the best currently known algorithms, such as factoring integers by Shor’s algorithm or the simulation of quantum many-body systems.

These lectures are oriented toward a wider audience, including young researchers, who have interests in the future quantum technologies, in particular in the fields of quantum algorithms and quantum simulations as well as other theoretical issues. Here is the recent progress of quantum computers announced by IBM: “We have successfully built a 20-qubit and a 50-qubit quantum processor that works”, “IBM Edges Closer to Quantum Supremacy with 50-Qubit Processor”.

Overview

1. Introduction
2. Quantum circuit model
2.1 Classical logic gates and classical circuit model
2.2 Quantum bits and gates
2.3 Quantum circuit model
2.4 Universality in quantum circuit model
2.5 Divincenzo’s criteria

3. Quantum computer: physical realization
3.1 NMR
3.2 Linear optics
3.3 Ion trap
3.4 quantum dots
3.5 Superconducting quibits.

4. Fighting with decoherence
4.1 Decoherence free subspace
4.2 Dynamical decoupling
4.3 Quantum error correction code (QECC)

5. Quantum Algorithms
5.1 Quantum Fourier transformation
5.2 Quantum phase estimation
5.3 Shor’s Algorithm

Reference
M. Nielson & I. Chuang, Quantum Computation and Quantum Information