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Quantum computing and the e ntanglement f rontier

Quantum computing and the e ntanglement f rontier. John Preskill APS April Meeting 15 April 2013. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31 :

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Quantum computing and the e ntanglement f rontier

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  1. Quantum computing and the entanglement frontier John Preskill APS April Meeting 15 April 2013

  2. George Gamow, recalling Bohr’s Theoretical Physics Institute 1928-31: Bohr’s Institute quickly became the world center of quantum physics, and to paraphrase the old Romans, “all roads led to Blegdamsvej 17” … The popularity of the institute was due both to the genius of its director and his kind, one might say fatherly, heart … Almost every country in the world has physicists who proudly say: “I used to work with Bohr.” Thirty Years That Shook Physics, 1966, p. 51.

  3. Werner Heisenberg on Schrödinger’s 1926 visit to Coperhagen: Bohr’s discussions with Schrödinger began at the railway station and continued daily from early morning until late at night. Schrödinger stayed at Bohr’s house so that nothing would interrupt the conversations … After a few days, Schrödinger fell ill, perhaps as a result of his enormous effort; in any case he was forced to keep to his bed with a feverish cold. While Mrs. Bohr nursed him and brought in tea and cake, Niels Bohr kept sitting on the edge of the bed talking at Schrödinger: “But surely you must admit that …” No real understanding could be expected since, at that time, neither side was able to offer a complete and coherent interpretation of quantum mechanics. Physics and Beyond, 1971, p. 73-76.

  4. Though quantum theory is over 100 years old, quantum and classical systems differ in profound ways we are just beginning to understand …

  5. Information is encoded in the state of a physical system.

  6. Information is encoded in the state of a quantum system.

  7. Put to work!

  8. Theoretical Quantum Information Science is driven by ... Three Great Ideas: 1) Quantum Entanglement 2) Quantum Computation 3) Quantum Error Correction

  9. Classical Bit

  10. Classical Bit

  11. Classical Bit What went in, comes out.

  12. Quantum Bit (“Qubit”) The two doors are two complementary observables, such as two ways to measure the polarization state of a photon.

  13. Quantum Bit (“Qubit”) If you open the same door that you closed, you can recover the bit from the box.

  14. Quantum Bit (“Qubit”)

  15. Quantum Bit (“Qubit”) If you open a different door than you closed, the color is random (red 50% of the time and green 50% of the time).

  16. No cloning!

  17. Photon polarization as a qubit

  18. Quantum Correlations Pasadena Andromeda Open either door in Pasadena, and the color of the ball is random. Same thing in Andromeda.

  19. Quantum Correlations Pasadena Andromeda But if we both open the same door, we always find the same color.

  20. Quantum Correlations Pasadena Andromeda Quantum information can be nonlocal, shared equally by a box in Pasadena and a box in Andromeda. This phenomenon, called quantum entanglement, is a crucial feature that distinguishes quantum information from classical information.

  21. ClassicalCorrelations

  22. Classical Correlations Quantum Correlations Aren’t boxes like soxes?

  23. Einstein’s 1935 paper, with Podolsky and Rosen (EPR), launched the theory of quantum entanglement. To Einstein, quantum entanglement was so unsettling as to indicate that something is missing from our current understanding of the quantum description of Nature.

  24. “If, without in any way disturbing a system, we can predict with certainty … the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”

  25. “there is … no question of a mechanical disturbance of the system under investigation during the critical last stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behavior of the system.”

  26. “Another way of expressingthe peculiar situation is: the best possible knowledge of a whole does not necessarily include the best possible knowledge of its parts … I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought… By the interaction the two representatives [quantum states] have become entangled.” Erwin Schrödinger, Proceedings of the Cambridge Philosophical Society, submitted 14 August 1935

  27. Quantum Entanglement Pasadena Andromeda Bell ‘64

  28. Pasadena Andromeda Quantum information can be nonlocal; quantum correlations are a stronger resource than classical correlations. Bell ‘64

  29. Quantum entanglement B A x y correlated Alice and Bob play a cooperative two-player game. bits a b Goal: If they share correlated classical bits and play their best strategy, they win with probability 75% (averaged over the inputs they receive).

  30. Quantum entanglement B A x y entangled Alice and Bob play a cooperative two-player game. qubits a b Goal: If they share entangled qubits and play their best strategy, they win with probability 85.4% (averaged over the inputs they receive).

  31. B A Quantum entanglement x y In experimental tests, physicists have played the game and have won with probability above 75%. entangled qubits a b Goal: Quantum correlations are a stronger resource than classical correlations. Aspect

  32. B A SpukhafteFernwirkungen!!* Quantum entanglement x y In experimental tests, physicists have played the game and have won with probability above 75%. entangled qubits a b Goal: Quantum correlations are a stronger resource than classical correlations. * Spooky action at a distance!!

  33. B A SpukhafteFernwirkungen!!* Sorry, Al . . . Quantum entanglement x y In experimental tests, physicists have played the game and have won with probability above 75%. entangled qubits a b Goal: * Spooky action at a distance!!

  34. Classical Correlations Quantum Correlations Boxes are not like soxes!

  35. Quantum entanglement …. …. This Page Blank This Page Blank This Page Blank This Page Blank This Page Blank Nearly all the information in a typical entangled “quantum book” is encoded in the correlations among the “pages”. You can't access the information if you read the book one page at a time.

  36. To describe 300 qubits, we would need more numbers than the number of atoms in the visible universe!

  37. We can’t even hope to describe the state of a few hundred qubits in terms of classical bits. Might a computer that operates on qubits rather than bits (a quantum computer) be able to perform tasks that are beyond the capability of any conceivable classical computer?

  38. Peter Shor

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

  40. 1807082088687 4048059516561 6440590556627 8102516769401 3491701270214 5005666254024 4048387341127 5908123033717 8188796656318 2013214880557 4553449864673 5972188403686 8972744088643 5630126320506 9600999044599 3968599945959 7454290161126 1628837860675 7644911281006 4832555157243 = ´ Finding Prime Factors The boundary between “hard” and “easy” seems to be different in a quantum world than in a classical world. Shor

  41. Factor 193 digits in 30 CPU years (2.2 GHz). Factor 500 digits in 1012 CPU years. Peter Shor Classical Computer Quantum Computer Factor 193 digits in 0.1 second. Factor 500 digits in 2seconds.

  42. Ron RivestAdi Shamir Len Adleman

  43. Problems Quantumly Hard Quantumly Easy Classically Easy

  44. Problems Quantumly Hard Quantumly Easy Classically Easy What’s in here?

  45. Quantum algorithms Quantum computers have limitations: Spectacular quantum speedups seem to be possible only for problems with special structure, notfor NP-complete problems like 3-SAT. (Quantum physics speeds up unstructured search quadratically, not exponentially.) Quantumly Hard Quantumly Classically Easy Easy Beyond NP: Speedups for problems outside NP are also common and important. Indeed the “natural” application for a quantum computer is simulating time evolution of quantum systems, e.g. collisions in molecular chemistry or quantum field theory. Many more quantum algorithms at math.nist.gov/quantum/zoo/

  46. Quantum algorithms for quantum field theories Classical methods have limited precision, particularly at strong coupling. A quantum computer can simulate particle collisions, even at high energy and strong coupling, using resources (number of qubits and gates) scaling polynomially with precision, energy, and number of particles. • Does the quantum circuit model capture the • computational power of Nature? • What about quantum gravity? • Jordan, Lee, Preskill, SCIENCE, 336: 1130, 1 JUNE 2012

  47. ( + ) ( + ) Environment Decoherence

  48. ( + ) ( + ) Environment Decoherence Decoherence explains why quantum phenomena, though observable in the microscopic systems studied in the physics lab, are not manifest in the macroscopic physical systems that we encounter in our ordinary experience.

  49. Quantum Computer Environment Decoherence How can we protect a quantum computer from decoherence and other sources of error? ERROR!

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