1. Quantum Information Science
QIS
Quantum
Computer

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

7. ? ? = ´ Finding Prime Factors = ? ?

8. = ´ Finding Prime Factors Shor ‘94 =
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. No tapping a quantum telephone!!
Alice
Eve
Bob
No tapping a quantum telephone!!

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

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

14. Quantum Error Correction

15. Quantum Error Correction

16. Quantum Error Correction

17. Quantum Error Correction
Redundancy protects against quantum errors!

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

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

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

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

22. Hamiltonian ?
rout

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

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

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

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

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

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

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

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

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

32. Ion Trap Quantum Computer
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. Is there a sharp boundary?
Quantum vs. Classical
Very
Quantum
Classical
Is there a sharp boundary?
Where is it?

35. Octahedral Computation
Bloch Sphere

36. Octahedral Computation
inscribed
octahedron
inscribed
octahedron

37. Controlled-NOT Gate a b a
a b

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

39. Octahedral Computation

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

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

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

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

44. Y AB A B M
copies

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

46. Local
Operations
Local
Operations
Classical M
copies
Communication

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

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

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

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

51. Fermilab Planckatron 103 GeV 1019 GeV !? 1016 in energy,
1032 in luminosity ..

52. Q
Feynmanlab

53. Using quantum mechanics, a device can be built that can handle information in a way no classical machine will be able to reproduce, such as the determination of the prime factors of very large numbers in an amount of time not much more than what is needed to do multiplications and other basic arithmetic with these large numbers. If our theory is right, it should be possible to mimick such a device using a classical theory. This gives us a falsifiable prediction:
‘t Hooft
It will never be possible to construct a `quantum computer’ that can factor a large number faster, and within a smaller region of space, than a classical machine would do, if the latter could be built out of parts at least as large and as slow as the Planckian dimensions.

54. This theoretical failure to find a plausible alternative to quantum mechanics … suggests to me that quantum mechanics is the way it is because any small changes in quantum mechanics would lead to absurdities.
Weinberg

55. Concatenated Quantum Coding
Each box, when examined with higher
resolution, is itself a block of five boxes.

56. Unitarity Deviations from Unitarity (e.g, decoherence) fine resolution
coarser
resolution
still
coarser
resolution
Unitarity

57. Is Nature fault-tolerant? intrinsic Unitarity Deviations from
fine
resolution
Are the laws of
physics attracted
to quantum mechanics
in the infrared?
Deviations
from
Unitarity
(e.g,
intrinsic
decoherence)
coarser
resolution
Hawking ‘75
Is Nature
fault-tolerant?
still
coarser
resolution
Unitarity

58. The 1st Quantum Century:
What happened after 1926?
We learned more about the Hamiltonian of the world:
Standard model, M-theory (?) …
We learned new tools for inferring its consequences:
Renormalization group, broken symmetries ..
and ….
We began to appreciate the implications of the tensor product structure of Hilbert space:
Quantum algorithms,
Quantum error correction,
...

59. Quantum Information Science
… is much more than a faster way to factor!
An enduring place at the core of computer science:
Cryptography
Computational complexity
Communication complexity
Error correction, fault-tolerance
Great Ideas destined for wider application:
Precision measurement
Quantum-classical boundary
Many-particle entanglement
A uniquely interdisciplinary community that should be nurtured.

60. Quantum Information Science
QIS
Quantum
Computer