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Quantum Information Science

Quantum Computer. Quantum Information Science. QIS. The Quantum Century. Y(1.9)K. Y2K. Shor. Planck. Three. Great Ideas!. (1) Quantum Computation. Feynman ‘81. Deutsch ‘85. Shor ‘94. Feynman ‘81. Deutsch ‘85. Shor ‘94.

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Quantum Information Science

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  1. Quantum Computer Quantum Information Science QIS

  2. The Quantum Century

  3. Y(1.9)K Y2K Shor Planck

  4. Three Great Ideas!

  5. (1) Quantum Computation Feynman ‘81 Deutsch ‘85 Shor ‘94

  6. Feynman ‘81 Deutsch ‘85 Shor ‘94 A computer that operates on quantum states can perform tasks that are beyond the capability of any conceivable classical computer.

  7. Finding Prime Factors 1807082088687 4048059516561 6440590556627 8102516769401 3491701270214 5005666254024 4048387341127 5908123033717 8188796656318 2013214880557 = ? ´ ?

  8. 1807082088687 4048059516561 6440590556627 8102516769401 3491701270214 5005666254024 4048387341127 5908123033717 8188796656318 2013214880557 4553449864673 5972188403686 8972744088643 5630126320506 9600999044599 3968599945959 7454290161126 1628837860675 7644911281006 4832555157243 = ´ Finding Prime Factors Shor ‘94

  9. (2) Quantum Key Distribution Bennett Brassard ‘84

  10. Eavesdropping on quantum information can be detected; key distribution via quantum states is unconditionally secure. Bennett Brassard ‘84

  11. Alice Eve Bob No tapping a quantum telephone!!

  12. (3) Quantum Error Correction Shor ‘95 Steane ‘95

  13. Quantum information can be protected, and processed fault-tolerantly. Shor ‘95 Steane ‘95

  14. Quantum Error Correction

  15. Quantum Error Correction Error!

  16. Quantum Error Correction

  17. Quantum Error Correction Redundancy protects against quantum errors!

  18. Three Great Ideas: 1) Quantum Computation 2) Quantum Key Distribution 3) Quantum Error Correction Where will they lead? Challenges for 21st century science!

  19. Thorne Caves Kimble Quantum information and precision measurement LIGO III: Beyond the standard quantum limit in 2008?!

  20. Quantum Information and Precision Measurement • New strategies for the • physics lab, exploiting: • quantum entanglement • quantum information processing • quantum error correction • etc.

  21. Hamiltonian ? rin rout Unknown classical force = mystery Hamiltonian (or master equation)

  22. rout Hamiltonian ?

  23. Hamiltonian ? Measure (Classical) Outcome Inference about H

  24. rin rout Hamiltonian ? How should we “query” the box to extract “optimal” information?

  25. rin rout Hamiltonian ? Drive the box: H = H? + HDrive Cf. Grover

  26. Bloch sphere Entangled Strategies Gather More Information Which way does the spin point?

  27. anti-parallel parallel Entangled Strategies Gather More Information Which way does the spin point? Compare: vs. Gisin, Popescu

  28. Zoller Ion Trap Quantum Computer I. Cirac, P. Zoller

  29. Zoller Ion Trap Quantum Computer I. Cirac, P. Zoller

  30. Zoller Ion Trap Quantum Computer I. Cirac, P. Zoller

  31. Zoller Ion Trap Quantum Computer I. Cirac, P. Zoller

  32. Zoller Ion Trap Quantum Computer I. Cirac, P. Zoller

  33. Experimental Challenges: • Read out single qubits. • Controlled coherent multi-qubit interactions. • Controlled fabrication. • etc. From ions, photons, atoms to nuclei, electrons. What quantum states and operations are useful and/or important?

  34. Very Quantum Very Classical Is there a sharp boundary? Where is it? Quantum vs. Classical

  35. Bloch Sphere Octahedral Computation

  36. inscribed octahedron inscribed octahedron Octahedral Computation

  37. a b a a b Controlled-NOT Gate

  38. Octahedral Computation Suffices for quantum error correction. Not universal quantum computation. Can be efficiently simulated on classical computer. Knill

  39. Octahedral Computation

  40. Conjecture (Kitaev): A reservoir of quantum states outside the octahedron Universal quantum computation Octahedral Computation r The “boundary” is the octahedron..

  41. Very Quantum Very Classical Is there a sharp boundary? Where is it? Quantum vs. Classical

  42. High T unentangled: A probability distribution ofclassical spins. Quantum vs. Classical Ensemble quantum computing at high temperature (e.g., liquid state NMR). But … entangling operations. Efficient classical simulations possible? A hierarchy of computational models? Knill, Laflamme, Caves, ...

  43. Y AB B A Multiparticle Entanglement How to characterize it and quantify it, for pure states. Cf., two qubits:

  44. Y AB Y AB Y AB Y AB Y AB B B B B B A A A A A M copies

  45. Y AB Y AB Y AB Y AB Y AB B B B B B A A A A A Local Operations Local Operations M copies

  46. Classical Communication Local Operations Local Operations M copies

  47. EPRAB EPRAB EPRAB N copies (N < M) B B B A A A Bennett, et al....

  48. ( )M Y AB EPRAB B A B A ( )N Two party pure-state entanglement can be converted to a standard currency (EPR pairs) … and back again.

  49. A A B C B C 3 EPR pairs 2 “cat” (GHZ) states But what about 3 (or more) part pure-state entanglement? Unknown whether these are (asymptotically) interchangeable. Popescu, Bennett, ...

  50. 1 2 3 4 m ? m-cats (m-1)-cats (m-2)-cats 2-cats Standard form: Many particles Quantum critical phenomena: how entangled is the ground state? Quantum dynamics: how hard to simulate (classically)?

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