# 1 Introduction to Quantum Computation and Quantum Information Dr. Raja Nagarajan University of Warwick.

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1 Introduction to Quantum Computation and Quantum Information Dr. Raja Nagarajan University of Warwick

2 Introduction Quantum Computing uses the theory of quantum physics as a foundation for a radically new approach to information processing.

3 Features of Quantum Computing It allows for large-scale parallelism Gives a tremendous speedup to some kinds of computation Permits perfectly secure transmission of information

4 The Quantum Bit In classical computers, the unit of information is a bit, which can be either 0 or 1. In quantum computers, the unit of information is a qubit, which can be in a superposition of 0 and 1.

5 Photons with a given Horizontal or Vertical Polarization Electrons with a given spin (up or down) The Hydrogen Atom, with its Ground and Excited States Qubits in Nature

6 Measurement In order to find out about a quantum state, we need to make a measurement or observation Measurement collapses states to basis states

7 The No-cloning Principle Unknown Quantum States cannot be copied.

8 Multiplication vs. Factoring 3 5 = 21 = Which of the above two problems is harder in general?

9 Factoring 29083 = Factoring is very hard on classical computers But it can be done efficiently on quantum computers

10 The Searching Problem Searching an unordered list containing N items On a classical computer: O(N) On a quantum computer: O( N) 1000000 1000

11 Cryptography Normandy Beach Alice Bob qrupdqgb ehdfk

12 Cryptographic Keys Keys can be learned by: searching (DES) factoring (RSA) If quantum computers are built, much of current computer security technology will become invalid.

13 Making Quantum Computers Quantum Computers can be built Prototypes do exist 57 qubits

14 Quantum Cryptography Fortunately, quantum cryptographic techniques have been developed These can be used to encrypt messages and they are secure even against quantum computers!

15 The Answers… Factoring: 127 x 229 = 29083 Code: Caesars cipher

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