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Quantum Computing

Paola Cappellaro Massachusetts Institute of Technology. Quantum Computing. Physics and Information. Information is stored in a physical medium and manipulated by physical processes. The laws of physics dictate the capabilities of any information processing device

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Quantum Computing

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  1. Paola Cappellaro Massachusetts Institute of Technology Quantum Computing

  2. Physics and Information • Information is stored in a physical medium and manipulated by physical processes. • The laws of physics dictate the capabilities of any information processing device Why not exploit quantum mechanics?

  3. Are computers already quantum? • Circuit components approach quantum size • Moore’s Law*sets limits to classical computation * ”The number of transistors incorporated in a chip will approximately double every 24 months”, Gordon Moore, Intel Co-founder (1965) Feature size (mm)

  4. Quantum Computation • Information is stored in 2-level physical systems • Classical bits: 0 or 1 • Quantum bits: |0 or |1 • QUBITS can also be in a superposition state a|0+ b|1 with |a|2 the probability of being in state |0

  5. Quantum Weirdness: Interference • A simple optic experiment: beam splitter 50% Detector 50% Single photon source Beam splitter Detector

  6. Classical Probability • Random coin flip: 50/50 probability 50% 50%

  7. Quantum Interference • A simple optic experiment:interferometer Mirror ?? % Single photon source Beam splitter Mirror

  8. Classical Probability • Random coin flip: 50/50 probability 50% 50%

  9. Quantum Interference • A simple optic experiment:interferometer Mirror ?? % Single photon source Beam splitter Mirror

  10. Quantum Interference • A simple optic experiment:interferometer Mirror Single photon source Beam splitter Mirror

  11. Quantum Interference • A simple optic experiment:interferometer Mirror Single photon source Beam splitter Mirror

  12. Quantum Interference • A simple optic experiment:interferometer Mirror Single photon source Beam splitter Mirror

  13. Quantum Interference • A simple optic experiment:interferometer Mirror Single photon source Beam splitter Mirror

  14. Quantum Interference • A simple optic experiment:interferometer 100 % Mirror 0 % Single photon source Beam splitter Mirror

  15. Quantum Weirdness: Interference In quantum mechanics we can make sure that the hiker (the photon) always reaches the cabin!

  16. Quantum Weirdness: Superposition

  17. Quantum Superposition 2 qubits can be in 4 states at the SAME time Need 4 parameters to describe the states • a|00+ b|01+ g|10+d|11

  18. Quantum Superposition

  19. Quantum Superposition

  20. Quantum Superposition

  21. Quantum Superposition

  22. Quantum Superposition

  23. The Power of Quantum Computers • Quantum superposition ➙ parallel computation • Example: quantum “oracle” wave-function collapse n qubits • f(a) N=2n states “oracle” tests all possible answers at once but answers cannot be read out

  24. The power of Quantum Computers • Qt. superposition ➙parallel computation • Qt. interference ➙ oracle is always right wave-function collapse interference n qubits N=2n states Paths leading to incorrect answers interfere destructively Only the right answer is left upon measurement

  25. Quantum speed-up • Exponentially faster computations • BUT: only for some algorithms • Applications: • Database search • Factorization ( = code breaking) … • Simulations of (quantum) systems • Precision measurement, secure communication, …

  26. Implementations • Need a physical qubit: • Two level quantum system ! Trapped ions

  27. Implementations • Need a physical qubit: • Two level quantum system ! Trapped atoms

  28. Implementations • Need a physical qubit: • Two level quantum system ! Superconducting circuit

  29. Implementations • Need a physical qubit: • Two level quantum system ! Semiconductor Quantum dots

  30. Implementations • Need a physical qubit: • Two level quantum system ! Nuclear & Electronic spins

  31. Diamond Quantum Computer • Electronic spin of the NV defect in diamond • Optical initialization and readout • Microwave control

  32. Logical gates and circuits

  33. Classical Gates Classical computers • NOT : 0 ➞ 1 or 1 ➞ 0 • AND: 2 inputs ⇓ 1 output

  34. Quantum Gates Quantum computers • NOT : ⎟0〉 ➞⎟1〉 or ⎟1〉➞⎟0〉 • CNOT: 2 inputs ⇓ 2 outputs

  35. Quantum Gates • Implementation by precise control of a quantum system: • New theoretical and technical tools required Bz

  36. Quantum Gates • Implementation by precise control of a quantum system: • New theoretical and technical tools required Bz

  37. Challenges • Quantum systems are fragile • No quantum weirdness in everyday life • Interaction with environment destroys the quantum superposition • Loss of quantum speedup • Challenges worsen with system size Scalability Decoherence

  38. Conclusions • Great promise but greater challenges • When will we have the first quantum computer? • In the meantime: • Better knowledge of quantum mechanics • Applications to • Precision measurements • Simulations • Communications

  39. Nuclear Science & Engineering

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