## Welcome to Introduction to Quantum Computing

The Lecturers for this course are Dr. Petros Wallden and Dr. Raul Garcia-Patron.

Quantum computation is a new paradigm of computation that has the potential to circumvent limitations of traditional computing devices for targeted applications as deciphering encrypted messages, simulating quantum systems or solving optimization problems. Devices build by major players in the computing industry are starting to challenge their classical counterparts, which has created a bourgeoning ecosystem of industry, start-up and academia. The aim of this course is to provide you with the tools to understand the basic principles of quantum computation and its main applications, preparing yourself for a career in the nascent quantum computing industry or a PhD program on the topic.

Learning Outcomes

On successful completion of this course, you should be able to:

1. use the mathematical framework of quantum computation to predict outcomes of quantum circuits

2. explain and analyse quantum algorithms described in quantum circuit and measurement-based quantum computing models

3. discuss the difference of performance between classical and quantum computer for different computational tasks

4. master notions of more advanced topics, such as error correction on algorithms for near-term architectures.

5. critically read and understand scientific literature on quantum computing.

### Course Aims

The aim of this course is to give students a basic overview of the rapidly growing field of Quantum Computation. The course will start with a brief introduction of the mathematical framework of quantum computation. This will be the opportunity to present some of the peculiarities of quantum mechanics, such as entanglement or the concept of measurement. After introducing the circuit model of quantum computation we will present a serie of quantum subroutines of historical but also practical importance. Finaly, after a short introduction to quantum error correcting codes, we will introduce two recent topics, algorithms for near-term quantum computers and the measurement-based quantum computing, the latest palying an important role in the theory of verification of quantum computation.

### Course Outline

- Basic concepts from Linear Algebra necessary for understanding the axioms of Quantum Mechanics,

- Axioms of Quantum Mechanics, describing quantum system, quantum operators, composition, entanglement and measurements

- Quantum Computing via quantum circuit model: Description of qubit and universal set of gates.

- The first quantum protocols: Quantum teleportation and super dense coding

- Quantum subroutines such as Phase Kick-back, Quantum Fourier Transform or Phase-Estimation

- Quantum Algorithms such as Grover's Search, Deutsch-Jozsa, Bernstein-Vazirani or Shor.

- Quantum Computing via measurement-based model: Description of graph state and measurement calculus

- Advanced Topics: quantum error correction, algorithm for near-term architectures, unconditionally secure quantum cloud computing

License

All rights reserved The University of Edinburgh