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

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

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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

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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.

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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

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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

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

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

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

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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

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11 Cryptography Normandy Beach Alice Bob qrupdqgb ehdfk

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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.

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

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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!

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

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