Quantum Computing

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Quantum Computing

  1. 1. ENGINEERING PHYSICS II
  2. 2. QUANTUM COMPUTER EVOLUTION LIES A HEADPRESENTED BY : P.SAI VARUN T.MURALI KRISHNA (1St Year) C.S.E Branch
  3. 3. CONTENTS Quantum Theory Influence of Quantum Theory Quantum Mechanics Two Slit Experiment with Electrons Applications
  4. 4. In 1900, physicist Max Planck presented his Quantum Theory to the German Physical Society. Max Planck 1858-1947Quantum theory:Quantum theory is the theoretical basis of modern physics thatexplains the nature and behavior of matter and energy on theatomic and subatomic level.
  5. 5. INFLUENCE OF QUANTUM THEORYEvolution of the Materials Bombs PowerUniverse Medical & Uses Technolog SUB ATOMIC y ATOMS & NUCLEAR PHYSICS PARTICLES MOLECULES QUANTUM THEORY QUANTUM OPTICS QUANTUM Quantum COMPUTIN Laser Communications Cryptography G s
  6. 6. QUANTUM MECHANICSQuantum mechanics is used to explain microscopic phenomenasuch as photon-atom scattering and flow of the electrons in asemiconductor.
  7. 7. QUANTUM MECHANICS is a collection of postulates based on ahuge number of experimental observations.
  8. 8. TWO SLIT EXPERIMENT Electrons 9
  9. 9. TWO SLIT EXPERIMENT Observing Electrons 10
  10. 10. APPLICATIONS OF QUANTUM MECHANICS TRANSISTORS The Transistors work on the unique properties of semiconductors -- materials that can act as either a conductor or an insulator -- to operate.
  11. 11. LASERSLasers work is by exciting the electrons orbiting atoms, which thenemit photons as they return to lower energy levels.The photons are released of the same energy level and direction,creating a steady stream of photons we see as a laser beam.
  12. 12. QUANTUM COMPUTERA quantum computer is a machine that performs calculations based onthe laws of Quantum Mechanics, which is the behavior of particles atthe sub-atomic level.Quantum Computer has the potential to perform calculationsbillions of times faster than silicon-based computer
  13. 13. CONTENTS History of Quantum Computer Quantum Computer Principle Basic Quantum Computation Bits Vs Qubits Bloch Sphere Quantum Gates
  14. 14. HISTORY OF QUANTUM COMPUTERSPaul Benioff is credited with first applying Quantum theory tocomputers in 1981.Quantum Computer was first discovered by Richard Feynmanin 1982.David Albert made the second discovery in 1984 when he described aself measuring quantum automaton. David Deutsch was made the most important quantum computing in1989.The finite machine obeying the laws of quantum computation arecontained in a single machine called as a „universal quantum computer‟.
  15. 15. QUANTUM COMPUTER PRINCIPLE Church-Turing PrincipleAlonzo Church Alan Turing(1903-1995) (1912-1954)“If There exists or can be built a universal quantum computer thatcan be programmed to perform any computational task that can beperformed by any physical object”.Every „function which would naturally be regarded as computable‟ can becomputed by the Universal Turing machine.
  16. 16. BASIC QUANTUM COMPUTATIONThe Qubit - can be 1, 0 or both 1 and 0representation for a quantum number is the “Ket”-‟I>‟|x> - number in Quantum ComputerSuperposition states: 2 N 1 2N 1 2 ai si Where: ai 1 i 0 i 0
  17. 17. EXAMPLES: 1 1 0 1 2 2 1 1 1 1 00 01 10 11 2 2 2 2
  18. 18. REPRESENTATION n Qubits: 2nx1 matrix represents the state: 1 |0> would be represented by 0 0 |1> would be represented by 1 1 2 Equal superposition would be 1 2
  19. 19. BITS VS QUBITSClassical bits are either 0 or 1Quantum bits “qubits” are in linear superposition of | 0> and | 1> 16 Qubits
  20. 20. Qubits and Quantum Registers
  21. 21. BLOCH SPHEREThe Bloch sphere is a geometric representation of qubit states aspoints on the surface of a unit sphere.
  22. 22. QUANTUM GATESQuantum Gates are similar to classical gates, but do not have adegenerate output. i.e. their original input state can be derived fromtheir output state, uniquely. They must be reversible.This means that a computation can be performed on a quantumcomputer only if it is reversible.In 1973,Charles Bennet shown that any computation can bereversible.
  23. 23. QUANTUM GATES ARE REVERSIBLEIn designing gates for a quantum computer, certainconstraints must be satisfied. A consequence of this requirement is that any quantum computing operation must be reversible. Reversible gates must have the same number of inputs and outputs.
  24. 24.  The most simple reversible classical gate is the infamous XOR (Exclusive or gate). In quantum computing it is usually called controlled-NOT or CNOT -gate. Observe that reversible (quantum) gates have equal number of inputs and outputs.
  25. 25. LOGIC GATES FOR QUANTUM BITS: 0 1 0 1 = 1 0 1 0 0 1 1 0 = 1 0 0 1
  26. 26. Quantum Logic Gates
  27. 27. QUANTUM GATES Hadamard Gate Controlled Not Gate (CN) Controlled Controlled Not Gate(CCN) Universal Quantum Gates Quantum Entanglement Quantum Teleportation
  28. 28. QUANTUM GATES - HADAMARDSimplest gate involves one qubit and is called a Hadamard Gate(also known as a square-root of NOT gate.) Used to put qubitsinto superposition. H H State |0> State |0> + |1> State |1> Note: Two Hadamard gates used in succession can be used as a NOT gate
  29. 29. QUANTUM GATES - CONTROLLED NOTA gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If the bit on the control line is 1, invertthe bit on the target line. Input Output A - Target A’ A B A’ B’ 0 0 0 0 B - Control B’ 0 1 1 1 1 0 1 0 1 1 0 1 Note: The CN gate has a similar behavior to the XOR gate with some extra information to make it reversible.
  30. 30. EXAMPLE OPERATION - MULTIPLICATION BY 2  We can build a reversible logic circuit to calculate multiplication by 2 using CN gates arranged in the following manner: Input Output Carry Ones Carry Ones Bit Bit Bit Bit 0 0 0 0 0 1 1 0 0 Carry Bit Ones Bit H
  31. 31. QUANTUM GATES - CONTROLLED CONTROLLEDNOT (CCN)A gate which operates on three qubits is called aControlled Controlled NOT (CCN) Gate. If the bits onboth of the control lines is 1,then the target bit is inverted. Input Output A B C A’ B’ C’ A - Target A’ 0 0 0 0 0 0 0 0 1 0 0 1 B - Control 1 B’ 0 1 0 0 1 0 0 1 1 1 1 1 C - Control 2 1 0 0 1 0 0 C’ 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1
  32. 32. A UNIVERSAL QUANTUM GATES  The CCN gate has been shown to be a universal reversible logic gate as it can be used as a NAND gate. A - Target Input Output A’ A B C A’ B’ C’ 0 0 0 0 0 0 B - Control 1 B’ 0 0 1 0 0 1 0 1 0 0 1 0 C - Control 2 C’ 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1When our target input is 1, our target 1 1 0 1 1 0output is a result of a NAND of B and C. 1 1 1 0 1 1
  33. 33. OTHER 1*1 UNITARY GATES (QUANTUM) 1 1 1Hadamard H 2 1 1 Pauli-X X 0 1 1 0 Classical inverter 0 i Pauli-Y Y i 0 1 0 Pauli-Z Z 0 1
  34. 34. OTHER 1*1 UNITARY GATES (QUANTUM) 1 0 Phase S 0 i 1 0 /8 T i /4 0 e
  35. 35. 2*2 UNITARY GATES 1 0 0 0Controlled-Not 0 1 0 0(Feynman) 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 swap 0 1 0 0These are counterparts of standard logic 0 0 0 1because all entries in arrays are 0,1
  36. 36. 2*2 UNITARY GATESThese are truly quantumlogic gates because not Controlled-Zall entries in arrays are0,1 1 0 0 0 Z 0 1 0 0 0 0 1 0 Another 0 0 0 1 symbol 1 0 0 0 0 1 0 0Controlled-phase 0 0 1 0 S 0 0 0 i
  37. 37. 3*3 UNITARY GATES This is a counterpart of standard logic because all entries in arrays are 0,1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 Toffoli 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
  38. 38. 3*3 UNITARY GATES abc This is a counterpart of standard logic because all entries in arrays are 0,1 1 0 0 0 0 0 0 0 abc 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 Fredkin 0 0 0 0 0 1 0 0This is one more notation for Fredkinthat some papers use 0 0 0 0 0 0 0 1
  39. 39. QUANTUM ENTANGLEMENT The fact that a quantum bit, qubit, can be in several states is called entanglement. An electron can have both spin up and down. When we try to measure the state of electron, it is found either as spin up or down, not both. The entanglement can be seen only when repeating the measurement. (with other electrons being in the same entangled state).
  40. 40. QUANTUM TELEPORTATION Teleportation means transmission of quantum states. That is quite difficult even if not impossible. That is used in telecommunication to protect telecommunication from eavesdropping (salakuuntelu) because the listening is not possible without destroying information...
  41. 41. QUANTUM MAN“I learned very early the difference between knowing thename of something and knowing something.” -Richard P. Feynman
  42. 42. “A person who never made a mistake never triedanything new.” -ALBERT EINSTEIN
  43. 43. Be a Hero .Always Say,“I Have No Fear.” -Swami Vivekananda
  44. 44. Thank s to theHumanities and Basic Sciences Physics DepartmentT.BHIMA RAJU SIR & K.DHANUNJAYA SIR
  45. 45. THANK YOU!

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