Quantum Computing - Basic Concepts

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Quantum Computing Basics

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Quantum Computing - Basic Concepts

  1. 1. (SOME INTRODUCTORY CONCEPTS) Presented by: Pangambam Sendash Singh M.Sc. Computer Science 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 1
  2. 2. Overview:  Introduction  Quantum properties  Data Representation  Some Basic Quantum Gates  Heroes of Quantum Computing  Conclusion  Reference 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 2
  3. 3. Introduction: What is Quantum Computing?  Calculation based on the laws of Quantum Mechanics.  Uses Quantum Mechanical Phenomena to perform operations on data.  Operations done at an atomic/sub-atomic level. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 3
  4. 4. Beauty of Quantum Theory:  Quantum Mechanical theories are totally different from the point of common sense.  But it agrees fully with experimental facts..  This is the beauty of Quantum Mechanics. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 4
  5. 5. Why Quantum Theory in Computing???  Classical(Newtonian) Mechanics deals with macroscopic system while Quantum Mechanics deals with microscopic system-atomic and subatomic level.  Computer system/components are becoming smaller and smaller from mechanical computer to vacuum tubes, to transistors then to IC’s that Classical theory fails to explain.  Thus Quantum theory becomes essential.. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 5
  6. 6. Quantum properties used:  Superposition  Decoherence  Entanglement  Uncertainty principle  Linear algebra  Dirac notation 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 6
  7. 7. Superposition:  Property to exist in multiple states.  In a quantum system, if a particle can be in states |A and |B, then it can also be in the state 1|A + 2|B ; 1 and 2 are complex numbers.  Totally different from common sense. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 7
  8. 8. Decoherence:  The biggest problem.  States that if a coherent (superposed) state interacts with the environment, it falls into a classical state without superposition.  So quantum computer to work with superposed states, it has to be completely isolated from the rest of the universe (not observing the state, not measuring it, ...) 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 8
  9. 9. Schrödinger's cat-a thought experiment: (Gives an idea about Superposition and Decoherence)  A cat and a flask of poison together in a shielded box.  Classically cat’s state: alive or dead.  Quantum Mechanical Interpretation:Cat is simultaneously alive or dead-Superposed State.  Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead-decoherence. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 9
  10. 10. Entanglement:  Most important property in quantum information.  States that two or more particles can be linked, and if linked, can change properties of particle(s) changing the linked one.  Two particles can be linked and changed each other without interaction. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 10
  11. 11. Uncertainty Principle:  Quantum systems are so small.  It is impossible to measure all properties of a Quantum system without disturbing it.  As a result there is no way of accurately predicting all the properties of a particle in a Quantum System. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 11
  12. 12. Linear algebra:  Quantum mechanics depends heavily on linear algebra.  Some of the Quantum Mechanical concepts come from the mathematical formalism, not experiments. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 12
  13. 13. Dirac Notation:  Dirac notation is used for Quantum Computing.  States of a Quantum system are represented by Ket vectors(Column Matrix).  Example: |0, |1  Other notation: Bra notation-Complex conjugate of Ket vectors(Row Matrix).  Example: 0|, 1|; 0|=|0†, 1|=|1† 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 13
  14. 14. Data representation:  Quantum Bit(Qubit) is used.  Qubit, just like ‘classical bit‘, is a memory element, but can hold not only the states |0 and |1 but also linear superposition of both states, α1|0+α2|1.  This superposition makes Quantum Computing fundamentally different. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 14
  15. 15.  Classical bit: {0, 1}  Qubit: {0, 1, superposed states of 0 and 1} Classical bit Vs Qubit: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 15
  16. 16. Physical representation of qubits:  A single atom that is in either Ground or Excited state.  Ground state representing |0 .  Excited state representing |1 . 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 16
  17. 17. Physical representation of qubits: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 17
  18. 18. More about qubits:  By superposition principle, a Qubit can be forced to be in a superposed state.  i.e. | = 1|0+ 2|1  Qubit in superposed state occupies all the states between |0 and |1 simultaneously , but collapses into |0 or |1 when observed physically.  A qubit can thus encode an infinite amount of information. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 18
  19. 19. Qubits in Superposed state: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 19
  20. 20. Operations on qubits:  Quantum logic gates are used.  Quantum logic gates are represented by Unitary Matrices-U†U=UU†=I.  States are also represented by matrices as: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 20
  21. 21. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 21
  22. 22. Hadamard Gate(SRN gate):  acts on a single qubit.  transforms |0 to (|0 +|1)/2  And |1 to (|0 -|1)/2 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 22
  23. 23. Pauli-X gate:  acts on a single qubit.  Quantum equivalent of NOT gate.  Transforms |1 to |0 and |0 to |1 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 23
  24. 24. Pauli-Y gate:  acts on a single qubit.  Transforms |1 to -i|0 and |0 to i|1 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 24
  25. 25. Pauli-Z gate:  acts on a single qubit.  Transforms |1 to -|1 and |0 remains unchanged. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 25
  26. 26. Phase shift gate:  acts on a single qubit.  Transforms |1 to ei |1 and |0 remains unchanged.  Modifies(rotates) the phase of quantum state by . 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 26
  27. 27.  There are also other quantum gates including Quantum Universal Gates which acts on two or more qubits.  viz: SWAP gate, CONTROLLED gates, TOFFOLI gates, FREDkiN gates, etc., etc. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 27
  28. 28. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 28
  29. 29. HEROES OF QUANTUM COMPUTING:  1981 -Richard Feynman determines that it is impossible to efficiently simulate an evolution of a quantum system on a classical computer. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 29
  30. 30. HEROES OF QUANTUM COMPUTING:  1985, David Deutsch, publishes a theoretical paper describing a Universal Quantum Computer. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 30
  31. 31. HEROES OF QUANTUM COMPUTING:  1994, Peter Shor-Used Entanglement and Superposition methods to find the Prime Factors of Integer(useful in quantum encryption technology). 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 31
  32. 32. HEROES OF QUANTUM COMPUTING:  1996 -Lov Grover(Indian American Computer Scientist, born at Meerut), invented Quantum Database Search Algorithm, very much faster one. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 32
  33. 33. HEROES OF QUANTUM COMPUTING:  1997 , David Cory, A.F. Fahmy,Timothy Havel, Neil Gershenfeld and Isaac Chuang publish the first papers on quantum computers based on bulk spin resonance, or thermal ensembles.  AND MANY MORE….. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 33
  34. 34. World's first Quantum Computer:  In 2007, a computer calledOrion was presented by D-Wave.  Technology in Orion, called “Adiabatic Quantum Computing", is based on superconducting electronics. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 34
  35. 35. A 16-qubit processor Some of the components of Orion OneofitsNoiseFilteringStage Orion chip’s sample holder, ready to begin a cooldown. It works at 0.005ºC above absolute zero (-273ºC) ChipconstructedbyD-WaveSystems 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 35
  36. 36. Applications: Physics Chemistry Material Science & Engineering Biology & Medicine Nanotechnology Business & Commerce Cryptography Large DBMS 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 36
  37. 37. Advantages:  Could process massive amount of complex data.  Ability to solve scientific and commercial problems.  Process data in a much faster speed.  Capability to convey more accurate answers.  More can be computed in less time. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 37
  38. 38. Disadvantages and Problems: Security and Privacy Issues:  Ability to crack down password (s).  Capability to break every level of encryption. Moral, ethical, social, and economic issues:  Growing too much dependency on machines.  Economic division: who can/cannot afford technology.  Not suitable for word processing and email.  Problem of Decoherence, the need of a noise free environment.  Complex hardware schemes like superconductors. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 38
  39. 39. Conclusions:  Quantum computer has more to offer.  Advantages outweighs disadvantages.  Wide range of applications. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 39
  40. 40. Conclusions:  “My students don’t understand Quantum Mechanics, because I don’t understand it. Nobody understand Quantum Mechanics.” Richard Feynman 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 40
  41. 41. References:  http://www.qubit.org  http://en.wikipedia.org/wiki/Quantum_computers  http://en.wikipedia.org/wiki/Quantum_gate  http://en.wikipedia.org/wiki/Timeline_of_quantum_computing  http://en.wikipedia.org/wiki/Quantum_mechanics  http://phys.educ.ksu.edu 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 41
  42. 42. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 42

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