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Quantum Information Science

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Title: Quantum Information Science


1
Quantum Information Science
QIS
2
The Quantum Century
3
Y(1.9)K
Y2K
Shor
Planck
4
Three
Great Ideas!
5
(1) Quantum Computation
6
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 81025167
69401 3491701270214 5005666254024 4048387341127 59
08123033717 8188796656318 2013214880557

?

?
8
Finding Prime Factors
Shor 94
9
(2) Quantum Key Distribution
10
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11
No tapping a quantum telephone!!
12
(3) Quantum Error Correction
13
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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
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
rin
rout
Unknown classical force mystery Hamiltonian
(or master equation)
22
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23
(Classical) Outcome
Inference about H
24
(No Transcript)
25
Cf. Grover
26
Entangled Strategies Gather More Information
Which way does the spin point?
27
Entangled Strategies Gather More Information
Which way does the spin point?
Compare
vs.
Gisin, Popescu
28
Ion Trap Quantum Computer
I. Cirac, P. Zoller
29
Ion Trap Quantum Computer
I. Cirac, P. Zoller
30
Ion Trap Quantum Computer
I. Cirac, P. Zoller
31
Ion Trap Quantum Computer
I. Cirac, P. Zoller
32
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
Quantum vs. Classical
35
Octahedral Computation
36
Octahedral Computation
37
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
Octahedral Computation
r
The boundary is the octahedron..
41
Quantum vs. Classical
42
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
Multiparticle Entanglement
How to characterize it and quantify it, for pure
states.
Cf., two qubits
44
M copies
45
Local Operations
Local Operations
M copies
46
Local Operations
Local Operations
M copies
47
Bennett, et al....
48
( )N
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?
Unknown whether these are (asymptotically)
interchangeable.
Popescu, Bennett, ...
50
Many particles
Quantum critical phenomena how entangled is the
ground state? Quantum dynamics how hard to
simulate (classically)?
51
Fermilab
103 GeV
1019 GeV !?
Planckatron
1016 in energy, 1032 in luminosity ..
52
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
Deviations from Unitarity (e.g, decoherence)
Unitarity
57
Are the laws of physics attracted to quantum
mechanics in the infrared?
fine resolution
Deviations from Unitarity (e.g,
intrinsic decoherence)
coarser resolution
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-part
icle entanglement A uniquely interdisciplinary
community that should be nurtured.
60
Quantum Information Science
QIS
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