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Quantum Information Science
QIS
Quantum
Computer
The
Quantum
Century
Y(1.9)K
Y2K
Planck
Shor
Three
Great
Ideas!
(1) Quantum
Computation
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.
Feynman ‘81
Deutsch ‘85
Shor ‘94
Finding Prime Factors
1807082088687
4048059516561
6440590556627
8102516769401
3491701270214
5005666254024
4048387341127
5908123033717
8188796656318
2013214880557
=
?

?
Finding Prime Factors
1807082088687
4048059516561
6440590556627
8102516769401
3491701270214
5005666254024
4048387341127
5908123033717
8188796656318
2013214880557
=
3968599945959
7454290161126
1628837860675
7644911281006
4832555157243

4553449864673
5972188403686
8972744088643
5630126320506
9600999044599
Shor ‘94
(2) Quantum
Key Distribution
Bennett
Brassard ‘84
Eavesdropping on quantum information can
be detected; key distribution via quantum
states is unconditionally secure.
Bennett
Brassard ‘84
Alice
Eve
Bob
No tapping a quantum telephone!!
(3) Quantum
Error Correction
Shor ‘95
Steane ‘95
Quantum information can be protected,
and processed fault-tolerantly.
Shor ‘95
Steane ‘95
Quantum Error Correction
Quantum Error Correction
Error!
Quantum Error Correction
Quantum Error Correction
Redundancy protects against quantum errors!
Three Great Ideas:
1) Quantum Computation
2) Quantum Key Distribution
3) Quantum Error Correction
Where will they lead?
Challenges for 21st century science!
Quantum information and precision measurement
LIGO III: Beyond the standard quantum limit in 2008?!
Thorne
Caves
Kimble
Quantum Information and Precision Measurement
New strategies for the
physics lab, exploiting:
•quantum entanglement
•quantum information processing
•quantum error correction
•etc.
rin
Hamiltonian
?
rout
Unknown classical force = mystery Hamiltonian
(or master equation)
Hamiltonian
?
rout
Hamiltonian
?
Inference about H
Measure
(Classical)
Outcome
rin
Hamiltonian
?
rout
How should we “query” the box to
extract “optimal” information?
rin
rout
Hamiltonian
?
Drive the box:
H = H? + HDrive
Cf. Grover
Entangled Strategies Gather More Information
Which way does
the spin point?
Bloch sphere
Entangled Strategies Gather More Information
Which way does
the spin point?
Compare:
vs.
parallel
anti-parallel
Gisin,
Popescu
Ion Trap Quantum Computer
I. Cirac, P. Zoller
Zoller
Ion Trap Quantum Computer
I. Cirac, P. Zoller
Zoller
Ion Trap Quantum Computer
I. Cirac, P. Zoller
Zoller
Ion Trap Quantum Computer
I. Cirac, P. Zoller
Zoller
Ion Trap Quantum Computer
I. Cirac, P. Zoller
Zoller
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?
Quantum vs. Classical
Very
Quantum
Very
Classical
Is there a sharp boundary?
Where is it?
Octahedral Computation
Bloch Sphere
Octahedral Computation
inscribed
octahedron
inscribed
octahedron
Controlled-NOT Gate
a
a
b
a b
Octahedral Computation
Suffices for quantum error correction.
Not universal quantum computation.
Can be efficiently simulated on classical computer.
Knill
Octahedral Computation
Octahedral Computation
r
Conjecture (Kitaev):
A reservoir of quantum states
outside the octahedron
Universal quantum computation
The “boundary” is the octahedron..
Quantum vs. Classical
Very
Quantum
Very
Classical
Is there a sharp boundary?
Where is it?
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, ...
Multiparticle Entanglement
How to characterize it and quantify it, for pure states.
Cf., two qubits:
A
Y
AB
B
A
A
M
copies
A
A
A
Y
AB
B
Y
AB
B
Y
AB
B
Y
AB
B
Y
AB
B
A
A
M
copies
A
Y
AB
B
Y
AB
B
Y
AB
B
Local
Y
Operations
A
A
Y
AB
AB
Local
B
Operations
B
Classical
M
copies
Local
Operations
Local
Operations
Communication
A
N
copies
(N < M)
A
A
E = lim M 
EPR
AB
B
EPR
AB
B
EPR
AB
B
NI
F
= S(r )
G
J
HM K
A
max
Bennett, et al....
(
A
Y
M
)
AB
B
(
A
EPR
AB
Two party pure-state entanglement can be
converted to a standard currency (EPR pairs)
… and back again.
N
)
B
But what about 3 (or more) part
pure-state entanglement?
A
A
B
C
3 EPR pairs
B
C
2 “cat” (GHZ) states
Unknown whether these are (asymptotically) interchangeable.
Popescu, Bennett, ...
Many particles
1
2 3
4
m
?
Standard
form:
m-cats
(m-1)-cats
(m-2)-cats
2-cats
Quantum critical phenomena: how entangled is the ground state?
Quantum dynamics: how hard to simulate (classically)?
Fermilab
103 GeV
1019 GeV !?
Planckatron
1016 in energy,
1032 in luminosity ..
Feynmanlab
Q
‘t Hooft
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:
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.
Weinberg
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.
Concatenated Quantum Coding
Each box, when examined with higher
resolution, is itself a block of five boxes.
Deviations
from
Unitarity
(e.g,
decoherence)
fine
resolution
coarser
resolution
still
coarser
resolution
Unitarity
Deviations
from
Unitarity
(e.g,
fine
resolution
coarser
resolution
Are the laws of
physics attracted
to quantum mechanics
in the infrared?
intrinsic
decoherence)
still
coarser
resolution
Unitarity
Hawking ‘75
Is Nature
fault-tolerant?
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,
...
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.
Quantum Information Science
QIS
Quantum
Computer