Introduction to Quantum Computation and Quantum Information Dr

Introduction l Quantum Computing uses theory of quantum physics as a foundation for a

Features of Quantum Computing l It allows for large-scale parallelism l Gives a tremendous

The Quantum Bit l In classical computers, the unit of information is a bit,

Qubits in Nature l l l Photons with a given Horizontal or Vertical Polarization

Measurement l l In order to find out about a quantum state, we need

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

Multiplication vs. Factoring 3 5 = 21 = Which of the above two problems

Factoring 29083 = l l Factoring is very hard on classical computers But it

The Searching Problem l l l Searching an unordered list containing N items On

Cryptography Alice qrup dqgb ehdf k Bob “Normandy Beach” 11

Cryptographic Keys can be learned by: l l searching (DES) factoring (RSA) If quantum

Making Quantum Computers l Quantum Computers can be built l Prototypes do exist l

Quantum Cryptography Fortunately, quantum cryptographic techniques have been developed These can be used to

The Answers… Factoring: Code: 127 x 229 = 29083 Caesar’s cipher 15

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

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

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

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

Qubits in Nature l l l 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 5

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

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

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

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

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

Cryptography Alice qrup dqgb ehdf k Bob “Normandy Beach” 11

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

Making Quantum Computers l Quantum Computers can be built l Prototypes do exist l 5— 7 qubits 13

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

The Answers… Factoring: Code: 127 x 229 = 29083 Caesar’s cipher 15