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Quantum Computing   UfUf H H H Nick Bonesteel Discovering Physics, Nov. 16, 2012.

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Presentation on theme: "Quantum Computing   UfUf H H H Nick Bonesteel Discovering Physics, Nov. 16, 2012."— Presentation transcript:

1 Quantum Computing   UfUf H H H Nick Bonesteel Discovering Physics, Nov. 16, 2012

2 What is a quantum computer, and what can we do with one?

3 A Classical Bit: Two Possible States 0

4 1

5 0 x y NOT x y Single Bit Operation: NOT

6 1 x y NOT x y Single Bit Operation: NOT

7 A Quantum Bit or “Qubit” 0

8 1

9 0

10 01

11 01 Quantum superposition of 0 and 1 A Quantum Bit or “Qubit”

12 1

13 01

14 0

15 A Quantum Bit: A Continuum of States sin cos   0 1 

16 A Quantum Bit: A Continuum of States   1 2 sin0 2 cos   i e   Actually, qubit states live on the surface of a sphere.

17 A Quantum Bit: A Continuum of States sin cos   0 1  But the circle is enough for us today.

18 A Quantum NOT Gate X

19 XX

20 X

21 XX

22 Hadamard Gate HH

23 HH

24 HH

25 HH

26 HH H is its own inverse

27 Hadamard Gate H is its own inverse HH

28 Hadamard Gate HH H is its own inverse

29 Hadamard Gate H is its own inverse HH

30 Fair Coin Trick Coin

31 Balanced Function Unbalanced Function or

32 UfUf A Two Qubit Subroutine to Evaluate f(x)

33 UfUf Input x can be either 0 or 1 Output is f(x) Initialize to state “0”

34 A Two Qubit Subroutine to Evaluate f(x) UfUf Input x can be either 0 or 1 This qubit can also be in state “1”

35 UfUf Bar stands for “NOT” 0 = 1, 1 = 0 A Two Qubit Subroutine to Evaluate f(x) Input x can be either 0 or 1 This qubit can also be in state “1”

36 UfUf UfUf Balanced Unbalanced or A Two Qubit Subroutine to Evaluate f(x)

37 A Quantum Algorithm (Deutsch-Jozsa ‘92) UfUf H H H

38 UfUf H H H

39 UfUf H H H

40 UfUf H H H

41 UfUf H H H

42 UfUf H H H Only ran U f subroutine once, but f(0) and f(1) both appear in the state of the computer! A Quantum Algorithm (Deutsch-Jozsa ‘92)

43 UfUf H H H If f is balanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

44 UfUf H H H If f is balanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

45 UfUf H H H If f is balanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

46 UfUf H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

47 UfUf H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

48 UfUf H H H If f is unbalanced: f(0) = f(1) and f(0) = f(1) A Quantum Algorithm (Deutsch-Jozsa ‘92)

49 UfUf H H H Unbalanced: Balanced: A Quantum Algorithm (Deutsch-Jozsa ‘92)

50 UfUf H H H Unbalanced: Balanced: A Quantum Algorithm (Deutsch-Jozsa ‘92)

51 UfUf H H H Unbalanced: Balanced: Measure top qubit A Quantum Algorithm (Deutsch-Jozsa ‘92)

52 UfUf H H H Unbalanced: Balanced: Measure top qubit A Quantum Algorithm (Deutsch-Jozsa ‘92)

53 UfUf H H H Unbalanced: Balanced: Measure top qubit A Quantum Algorithm (Deutsch-Jozsa ‘92)

54 One qubit H

55 HH Two qubits

56 HH Counting in binary Two qubits

57 HHH Three qubits

58 HHH

59 HHH H N N -1 … N qubits

60 HHH H Quantum superposition of all possible input states! N qubits

61 HHH H Quantum superposition of all possible input states! For N=250 the number of states is roughly the number of atoms in the universe! N qubits

62 HHH H Quantum superposition of all possible input states! For N=250 the number of states is roughly the number of atoms in the universe! UfUf One function call N qubits

63 HHH H Quantum superposition of all possible input states! For N=250 the number of states is roughly the number of atoms in the universe! UfUf One function call x can be any integer From 0 to 2 N -1 N qubits

64 HHH H Quantum superposition of all possible input states! UfUf One function call Evaluate f(x) for all possible inputs! x can be any integer From 0 to 2 N -1 N qubits

65 Massive Quantum Parallelism H H H H UfUf Only one problem: When I measure this state I only learn the value of f(x) for one input x. (No free lunch!) However, people have shown that a quantum computer can use quantum parallelism to do things no classical computer can do. Run program U f once, get result for all possible inputs!

66 Given two prime numbers p and q, p x q = C Easy C p, q Hard Best known classical factoring algorithm scales as time = exp(Number of Digits) Mathematical Basis for Public Key Cryptography. Prime Factorization

67 In 1994 Peter Shor showed that a Quantum Computer could factor an integer exponentially faster than a classical computer! time = (Number of Digits) Shor’s algorithm exploits Massive Quantum Parallelism. 3 Quantum Factorization

68 OK, so how do we make a quantum computer?

69 Boolean Logic Gates x y zx y NotNOR Any classical computation can be carried out using these two gates x y x y z

70 Transistor Logic A A A B A B

71 The Integrated Circuit Core i7: 731,000,000 transistors

72 Single Qubit Gates U

73 X X Controlled-NOT Gate X X

74 X X X X U U Any quantum computation can be carried out using these two gates Universal Set of Gates U X Quantum Circuit

75 2012 Nobel Prize in Physics Dave Wineland Serge Haroche

76 State of the Art: Superconducting Qubits From : “Quantum Computers,” T. D. Ladd et al., Nature 464, (2010)

77 High fidelity (~95%) 2-qubit gates on a time scale of 30 ns. Nature 460, (2009) 2 superconducting qubits coupled by a microwave resonator

78 Nature 460, (2009) 2 superconducting qubits coupled by a microwave resonator High fidelity (~95%) 2-qubit gates on a time scale of 30 ns.

79 8 mm First steps toward a scalable quantum computer From:

80 The Real Problem: Decoherence!

81 Qubit

82 The Real Problem: Decoherence! Qubit Everything else

83 The Real Problem: Decoherence! Qubit Everything else Over time….

84 The Real Problem: Decoherence! Qubit Everything else Over time…. Quantum coherence of qubit is inevitably lost!

85 The Real Problem: Decoherence! Qubit Everything else Over time…. Quantum coherence of qubit is inevitably lost! Amazingly enough, quantum computing is still possible using what is known as “fault-tolerant quantum computation.”

86 Coherence Times for Superconducting Qubits From: “Superconducting Qubits Are Getting Serious”, M. Steffen, Physics 4, 103 (2011) Threshold for fault- tolerant quantum computation.

87 From: “Superconducting Qubits Are Getting Serious”, M. Steffen, Physics 4, 103 (2011) Threshold for fault- tolerant quantum computation. This is what most of my own research on quantum computing is focused on. Coherence Times for Superconducting Qubits

88 A deep question: Do the laws of nature allow us to manipulate quantum systems with enough accuracy to build “quantum machines” ? Conclusions

89 A deep question: Do the laws of nature allow us to manipulate quantum systems with enough accuracy to build “quantum machines” ? If the answer is “yes” (as it seems to be), then quantum computers are coming! Conclusions


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