Physical Basics of Quantum Computing

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  • Statistical aspects of quantum mechanics
    • In this module we will briefly discuss the statistical aspects of quantum mechanics. We will discuss the difference between pure and mixed quantum states and consider their mathematical description. We will introduce the concept of a qubit and give some examples of its physical implementation. We will define what quantum entanglement (inseparability) is.
  • Quantum entanglement
    • We will continue the talk about quantum entanglement and consider mathematical criteria for the inseparability of quantum systems. We will speak about the Bell states that represent the simplest (and maximal) examples of quantum entanglement. The major part of this module will focus on the famous Einstein–Podolsky–Rosen paradox and the Bell inequality test, which are crucial for understanding the physical side of the concept.
  • Classical and quantum logical operations
    • Paying tribute to Alonzo Church and Alan Turing we will start this module with the talk about the Church–Turing thesis and the Turing machine. We will briefly recall how the classical elementary logic gates work and consider some classical logic circuits on their basis. This will allow us to draw important analogies with elementary quantum logic gates. After the discussion of Landauer's principle we will look at how to build classical and quantum circuits using only reversible logic gates.
  • Distinctive features of quantum computations
    • In this module, we will consider the most characteristic features of the transmission and processing of quantum information. We will prove why it is impossible to make a copy of a qubit in an arbitrary quantum state. We will see how two bits of classical information can be transmitted using a single qubit, implementing superdense coding. In addition, we will ake a closer look at the quantum teleportation protocol, which allows to transfer the state of a qubit over long distances. The last part of the module will be devoted to quantum parallelism, which allows a large number of quantum computations to be performed simultaneously.
  • Quantum algorithms
    • This module is the major one and the most important in the whole course. We will see how all the ideas we discussed earlier allow one to conduct quantum computing, which for certain problems will be more efficient than classical ones. We will consider the application of these ideas in the Deutsch and Deutsch-Jozsa algorithms. And at the end of the module, we will talk about widely discussed Shor's algorithm.
  • Basics of error correction theory
    • Since no computation is possible without errors, in the last module of the course, we will briefly talk about classical and quantum error correction.

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