Introduction to Quantum Computing

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Quantum Circuits • Can we make a Qubit Copying Circuit - How about copying a qubit in an unknown state using a controlled-CNOT gate ψ = a 0 + b 1 bit to be copied a 0 + b 1 Output State a 00 + b 10 0 a 00 + b 11 scratch-pad initialized to zero 46
Quantum Circuits • Can we make a Qubit Copying Circuit - Does ψ ψ = a 00 + b 11 ( )( ) 2 2 ψ ψ = a 0 + b 1 a 0 + b 1 = a 00 + ab 01 + ab 10 + b 11 - Unless ab = 0this does not copy the quantum state input 2 2 a 00 + ab 01 + ab 10 + b 11 ≠ a 00 + b 11 - It is impossible to make a copy of the unknown quantum state - NO CLONING THEOREM - 47
Page 1 and 2: Introduction to Quantum Computing L
Page 3 and 4: Why Quantum Computing 3
Page 5 and 6: Transistor Size Electrons per devic
Page 7 and 8: What is Quantum Computing 7
Page 9 and 10: Spin States • An electron is alwa
Page 11 and 12: Definitions • A qubit is governed
Page 13 and 14: Superposition Measurement • If th
Page 15 and 16: History • In the 1970’s s Fredk
Page 17 and 18: Quantum Weirdness 17
Page 19 and 20: Comparison I • Compare qubits to
Page 21 and 22: Quantum Phenomena 21
Page 23 and 24: Superposition • The Principal of
Page 25 and 26: Entanglement • If two or more qub
Page 27 and 28: Non-Clonability • It is impossibl
Page 29 and 30: Quantum Computation Changes to a qu
Page 31 and 32: Quantum Computation NOT gate repres
Page 33 and 34: Quantum Computation Two more import
Page 35 and 36: Quantum Computation • Review: Imp
Page 37 and 38: Quantum Computation • Classical U
Page 39 and 40: CNOT quantum gate ⎡1 0 0 0⎤ A A
Page 41 and 42: Quantum Circuits • Elements of a
Page 43 and 44: • Controlled-U U Gate Quantum Cir
Page 45: Quantum Circuits • Can we make a
Page 49 and 50: Quantum Algorithms Initial State (
Page 51 and 52: Quantum Algorithms • Deutsch's Al
Page 53 and 54: Quantum Algorithms • Deutsch's Al
Page 55 and 56: Quantum Algorithms • Deutsch-Jozs
Page 61 and 62: Quantum Algorithms • Other Quantu
Page 63 and 64: NMR Quantum Computing Lecture 2 63
Page 65 and 66: Nuclear Magnetic Resonance Q.C. Phy
Page 67 and 68: Internal Hamiltonian • The evolut
Page 69 and 70: Tomography Not all elements of the
Page 71 and 72: Outline • Introduction of quantum
Page 73 and 74: • Table: Payoff matrix for the Pr
Page 75 and 76: Interesting results For a separable
Page 77 and 78: A physical model of quantum game
Page 79 and 80: • Nash Equilibrium: Uˆ A ⊗Uˆ
Page 81 and 82: Experimental realization Physics Re
Page 83 and 84: Quantum network and gates • Quant
Page 85 and 86: NMR Spectrometer 85
Page 87 and 88: • Good agreement between theory a
Page 89 and 90: 2001.9: APS- Physics News Update 89
Page 91: Thanks 91

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