Introduction to Quantum Computation and Quantum Information

1
Introduction to Quantum Computation and Quantum
Information

• Dr. Raja Nagarajan
• University of Warwick

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Introduction

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

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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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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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Qubits in Nature

• 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

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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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The No-cloning Principle

• Unknown Quantum States cannot be copied.

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Multiplication vs. Factoring

• 3 ? 5 ?
• 21 ? ? ?
• Which of the above two problems is harder in
  general?

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Factoring

• 29083 ? ? ?
• Factoring is very hard on classical computers
• But it can be done efficiently on quantum
  computers

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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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Cryptography
Alice
Bob
qrupdqgb ehdfk
Normandy Beach
Normandy Beach
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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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Making Quantum Computers

• Quantum Computers can be built
• Prototypes do exist
• 57 qubits

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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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The Answers

• Factoring 127 x 229 29083
• Code Caesars cipher