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Quantum Computing - Basic Concepts

May 11, 2015

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Engineering

Quantum Computing Basics

  • 1.(SOME INTRODUCTORY CONCEPTS) Presented by: Pangambam Sendash Singh M.Sc. Computer Science 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 1

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. 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. 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. 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 ICs that Classical theory fails to explain. Thus Quantum theory becomes essential.. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 5 6. Quantum properties used: Superposition Decoherence Entanglement Uncertainty principle Linear algebra Dirac notation 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 6 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. 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. Schrdinger'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 cats 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. 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. 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. 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. 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. 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, 1|0+2|1. This superposition makes Quantum Computing fundamentally different. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 14 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. 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. Physical representation of qubits: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 17 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. Qubits in Superposed state: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 19 20. Operations on qubits: Quantum logic gates are used. Quantum logic gates are represented by Unitary Matrices-UU=UU=I. States are also represented by matrices as: 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 20 21. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 21 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. 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. 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. 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. 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. 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. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 28 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. 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. 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. 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. 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. 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. A 16-qubit processor Some of the components of Orion OneofitsNoiseFilteringStage Orion chips sample holder, ready to begin a cooldown. It works at 0.005C above absolute zero (-273C) ChipconstructedbyD-WaveSystems 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 35 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. 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. 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. Conclusions: Quantum computer has more to offer. Advantages outweighs disadvantages. Wide range of applications. 5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 39 40. Conclusions: My students dont understand Quantum Mechanics, because I dont