# quantum computing

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- 1.ENGINEERING PHYSICS II

2. QUANTUM COMPUTER EVOLUTION LIES A HEADPRESENTED BY :P.SAI VARUN T.MURALI KRISHNA (1St Year) C.S.E Branch 3. CONTENTS Quantum Theory Influence of Quantum Theory Quantum Mechanics Two Slit Experiment with Electrons Applications 4. In 1900, physicist Max Planck presented his Quantum Theory to the German Physical Society. Max Planck1858-1947Quantum 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. INFLUENCE OF QUANTUM THEORYEvolution of the Materials BombsPowerUniverse Medical & UsesTechnologSUB ATOMIC yATOMS & NUCLEAR PHYSICSPARTICLES MOLECULES QUANTUM THEORY QUANTUM OPTICSQUANTUM Quantum COMPUTIN LaserCommunications Cryptography Gs 6. QUANTUM MECHANICSQuantum mechanics is used to explain microscopic phenomenasuch as photon-atom scattering and flow of the electrons in asemiconductor. 7. QUANTUM MECHANICS is a collection of postulates based on ahuge number of experimental observations. 8. TWO SLIT EXPERIMENTElectrons9 9. TWO SLIT EXPERIMENT Observing Electrons 10 10. APPLICATIONS OF QUANTUM MECHANICSTRANSISTORS The Transistors work on the unique properties of semiconductors -- materials that can act as either a conductor or an insulator -- to operate. 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. 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. CONTENTS History of Quantum Computer Quantum Computer Principle Basic Quantum ComputationBits Vs Qubits Bloch Sphere Quantum Gates 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. QUANTUM COMPUTER PRINCIPLE Church-Turing PrincipleAlonzo ChurchAlan 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. 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 12N 12 ai siWhere: ai 1i 0i 0 17. EXAMPLES:11 01 22 1111 00 01 10 11 2222 18. REPRESENTATION n Qubits: 2nx1 matrix represents the state:1|0> would be represented by00|1> would be represented by1 12Equal superposition would be 12 19. BITS VS QUBITSClassical bits are either 0 or 1Quantum bits qubits are in linear superposition of | 0> and | 1> 16 Qubits 20. Qubits and Quantum Registers 21. BLOCH SPHEREThe Bloch sphere is a geometric representation of qubit states aspoints on the surface of a unit sphere. 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. 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. The most simple reversible classical gate is the infamousXOR (Exclusive or gate). In quantum computing it is usually called controlled-NOTor CNOT -gate. Observe that reversible (quantum) gates have equal numberof inputs and outputs. 25. LOGIC GATES FOR QUANTUM BITS:0 10 1 = 1 0 1 0 0 1 1 0 =1 00 1 26. Quantum Logic Gates 27. QUANTUM GATESHadamard GateControlled Not Gate (CN)Controlled Controlled Not Gate(CCN)Universal Quantum GatesQuantum EntanglementQuantum Teleportation 28. QUANTUM GATES - HADAMARDSimplest 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 insuccession can be used as a NOT gate 29. QUANTUM GATES - CONTROLLED NOTA 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 - ControlB 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. EXAMPLE OPERATION - MULTIPLICATIONBY 2 We can build a reversible logic circuit to calculate multiplication by 2 using CN gates arranged in the following manner: InputOutput Carry Ones Carry OnesBit BitBit Bit 00 00 01 10 0 Carry Bit Ones BitH 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 OutputA B C A B C A - TargetA 0 0 0 0 000 0 1 0 01B - Control 1B 0 1 0 0 100 1 1 1 11 C - Control 21 0 0 1 00 C1 0 1 1 011 1 0 1 101 1 1 0 11 32. A UNIVERSAL QUANTUM GATES The CCN gate has been shown to be a universal reversiblelogic gate as it can be used as a NAND gate.A - Target Input OutputA A B C A B C 0 0 0 0 00B - Control 1 B 0 0 1 0 01 0 1 0 0 10C - Control 2C 0 1 1 1 11 1 0 0 1 00 1 0 1 1 01When our target input is 1, our target 1 1 0 1 10output is a result of a NAND of B and C. 1 1 1 0 11 33. OTHER 1*1 UNITARY GATES (QUANTUM) 1 11Hadamard H2 1 1 Pauli-X X0 11 0Classical inverter0i Pauli-Y Yi 01 0Pauli-ZZ01 34. OTHER 1*1 UNITARY GATES (QUANTUM)1 0 Phase S0 i1 0 /8Ti /40 e 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 swap0 1 0 0These are counterparts of standard logic 0 0 0 1because all entries in arrays are 0,1 36. 2*2 UNITARY GATESThese are truly quantumlogic gates because not Controlled-Zall entries in arrays are0,1 1 0 00Z0 1 000 0 10Another0 0 01symbol 1 0 0 0 0 1 0 0Controlled-phase 0 0 1 0S 0 0 0 i 37. 3*3 UNITARY GATESThis is a counterpart of standard logicbecause all entries in arrays are 0,11 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 0Toffoli 0 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 0 10 0 0 0 0 0 1 0 38. 3*3 UNITARY GATESabc This is a counterpart of standard logic because all entries in arrays are 0,11 0 0 0 0 0 0 0 abc0 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 0 1 0Fredkin 0 0 0 0 0 1 0 0This is one more notation for Fredkinthat some papers use0 0 0 0 0 0 0 1 39. QUANTUM ENTANGLEMENT The fact that a quantum bit, qubit, can be in several states is calledentanglement. An electron can have both spin up and down. When we try to measure the state of electron, it is found either as spinup or down, not both. The entanglement can be seen only when repeating the measurement.(with other electrons being in the same entangled state). 40. QUANTUM TELEPORTATION Teleportation means transmission of quantum states. That is quitedifficult even if not impossible. That is used in telecommunication to protect telecommunicationfrom eavesdropping (salakuuntelu) because the listening is notpossible without destroying information... 41. QUANTUM MANI learned very early the difference between knowing thename of something and knowing something. -Richard P. Feynman 42. A person who never made a mistake never triedanything new.-ALBERT EINSTEIN 43. Be a Hero .Always Say,I Have No Fear.-Swami Vivekananda 44. Thank s totheHumanities and Basic Sciences Physics DepartmentT.BHIMA RAJU SIR & K.DHANUNJAYA SIR 45. THANK YOU!