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Quantum Information Science
Atomic-Molecular
Optical Physics
Condensed
Matter Physics
Exotic Quantum
States of Matter!
J. Preskill
3 Dec. 2008
Quantum Information Science
Planck
Turing
Shannon
Quantum physics, information
theory, and computer science
are among the crowning
intellectual achievements of
the 20th century.
Quantum information science
is an emerging synthesis of
these themes, which is
providing important insights
into fundamental issues at the
interface of computation and
physical science, and may
guide the way to revolutionary
technological advances.
Information
is encoded in the state of a physical system.
Information
is encoded in the state of a quantum system.
Put
to work!
Quantum Entanglement
classically correlated socks
quantumly correlated photons
• There is just one way to look at a classical bit (like the color of my sock),
but there are complementary ways to observe a quantum bit (like the
polarization of a single photon). Thus correlations among qubits are
richer and much more interesting than correlations among classical bits.
• A quantum system with two parts is entangled when its joint state is
more definite and less random than the state of each part by itself.
Looking at the parts one at a time, you can learn everything about a pair
of socks, but not about a pair of qubits!
The quantum correlations of many entangled qubits cannot be
easily described in terms of ordinary classical information. To give
a complete classical description of one typical state of just a few
hundred qubits would require more bits than the number of atoms
in the visible universe!
It will never be possible, even in principle to write down such a
description.
We can’t even hope to
describe the state of a few
hundred qubits in terms of
classical bits.
As Feynman first suggested
in 1981, a computer that
operates on qubits rather
than bits (a quantum
computer) can perform tasks
that are beyond the capability
of any conceivable digital
computer!
Finding Prime Factors
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
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An example of a problem that is hard for
today’s supercomputers: finding the factors
of a large composite number. Factoring
e.g. 500 digit numbers will be intractable
for classical computers even far into the
future.
Finding Prime Factors
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4048059516561
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8102516769401
3491701270214
5005666254024
4048387341127
5908123033717
8188796656318
2013214880557
=
3968599945959
7454290161126
1628837860675
7644911281006
4832555157243

4553449864673
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8972744088643
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9600999044599
But for a quantum computer, factoring is
not much harder than multiplication! The
boundary between the problems that are
“hard” and the problems that are “easy” is
different in a quantum world than a
classical world.
John Preskill
Physics
Jeff Kimble
Physics
Alexei Kitaev
Physics and
Computer Science
Gil Refael
Physics
Leonard Schulman
Computer Science
CENTER FOR
THE PHYSICS OF
INFORMATION
Former IQI Postdocs now in faculty positions elsewhere
Hallgren
Bacon
Bose
Nayak
Shi
Doherty
Geremia
Duan
Hayden
Terhal
Vidal
Leung
Bravyi
Verstraete
Wocjan
Childs
Raussendorf
Ardonne
Former IQI Postdocs now in faculty positions elsewhere
Penn State
Waterloo
Washington
Michigan
London
Waterloo
Michigan
Queensland
UNM
McGill
IBM
Queensland
IBM
Vienna
Waterloo
UBC
U. Cental Fla. Nordita
Some former IQI Students
Bob Gingrich (2001) – PIMCO
Andrew Landahl (2002) – University of New Mexico
Federico Spedalieri (2003) – UCLA
Sumit Daftuar (2003) – Goldman Sachs
John Cortese (2003) – LIGO (Caltech)
Charlene Ahn (2004) – Toyon Research Corporation
Dave Beckman (2004) – Toyon Research Corporation
Jim Harrington (2004) – Los Alamos National Laboratory
Carlos Mochon (2005) – Perimeter Institute
Anura Abeyesinghe (2006) – Univ. Central Florida
Graeme Smith (2006) – IBM
Ben Toner (2006) – CWI, Amsterdam
Panos Aliferis (2007) – IBM
Parsa Bonderson (2007) -- Microsoft Research
Mike Zwolak (2007) – Los Alamos National Laboratory
Ahn
Cortese Harrington Mochon Abeyesinghe Smith
Bonderson Zwolak
Gingrich
Landahl
Spedalieri
Daftuar
Toner
Aliferis
Quantum Information Challenges
Cryptography
Algorithms
 | x | f ( x)
xG
Privacy from physical principles
Error correction
What can quantum computers do?
Hardware
Quantum
Computer
Noise
Reliable quantum computers
Toward scalable devices
And …what are the implications of these ideas for basic physics?
Condensed matter physics
In a nutshell:
whole >  (parts)
Emergent phenomena: the collective behavior of many
particles cannot be easily guessed, even if we have complete
knowledge of how the particles interact with one another.
Entangled quantum many-particle systems have an enormous
capacity to surprise and delight us.
Fractional quantum Hall state
High temp. superconductor
Crystalline material
Emergence: the fractional quantum Hall effect
Highly mobile electrons, confined
to a two-dimensional interface
between semiconductors, and
exposed to a strong magnetic
field, find a very exotic highlyentangled quantum state (which
can be observed at sufficiently low
temperature).
Fractional quantum Hall state
The local excitations (“quasi-particles”) of this system are
profoundly different than electrons. In fact, a single quasiparticle carries an electric charge that is a fraction (for
example, 1/3) of the charge of an electron.
Is this the tip of an enormous iceberg?
Are such phenomena useful?
Topology
Quantum
Computer
Quantum
Computer
Noise!
F
F
F
Aharonov-Bohm
Phase
exp(ieF)
F
Aharonov-Bohm
Phase
exp(ieF)
Anyons
Quantum information can be stored in the collective state
of exotic particles in two dimensions (“anyons”).
The information can be processed by exchanging the
positions of the anyons (even though the anyons never
come close to one another).
Anyons
Quantum information can be stored in the collective state
of exotic particles in two dimensions (“anyons”).
The information can be processed by exchanging the
positions of the anyons (even though the anyons never
come close to one another).
Topological quantum computation
annihilate pairs?
braid
Kitaev
braid
braid
time
create pairs
Topological quantum computation
annihilate pairs?
braid
Kitaev
braid
braid
time
create pairs
Topological quantum computation
The computation is
intrinsically resistant
to noise.
If the paths followed
by the particles in
spacetime execute
the right braid, then
the quantum
computation is
guaranteed to give
the right answer!
time
Topological
quantum
computation
Physical fault tolerance
with nonabelian anyons
Kitaev
Eisenstein
“The rule of simulation that I
would like to have is that the
number of computer elements
required to simulate a large
physical system is only
proportional to the space-time
volume of the physical
system”
R. P. Feynman, “Simulating
Physics with Computers”
(1981).
Quantum simulators:
Condensed matter meets atomic physics
In general, we can’t
simulate a many-particle
quantum system with a
classical computer.
But we can simulate one
quantum system with
another one!
The atomic physicists have developed remarkable tools for
cooling and controlling atoms. Exploiting these tools, we can
study (and discover) quantum many-particle phenomena that up
until now have been experimentally inaccessible.
Crossover in fermion pair condensates
C. Regal et al. (2004) , M. Zwierlein et al. (2005)
Superfluidity persists through the crossover from a molecular condensate of
tightly bound pairs of fermionic (potassium or lithium) atoms (BEC) to a
condensate of loosely bound Cooper pairs (BCS) analogous to a
superconducting state of a system of electrons.
Because a superfluid flows without resistance, a rotating superfluid
organizes into vortices, each carrying a tiny fraction of the angular
momentum, and because the vortices repel one another, they crystalize into
a regular lattice. The strength of the interactions between fermionic atoms
can be modulated by varying a magnetic field, so that the crossover from (b)
to (c) can be studied experimentally.
Many-body physics with polar molecules
P. Zoller et al. (2006)
J. Ye et al. (2008)
Polar molecules, trapped in an optical lattice, have dipole moments, which
provide a useful handle for manipulating the interactions among the
molecules and realizing exotic quantum many-body states (for example, the
ground state of the Kitaev model, which supports nonabelian anyons).
How fast does information escape from a black hole?
Hayden,
Preskill
Bob decodes
black hole
Bob
Alice
radiation
black
hole
strongly
mixing
unitary
Black holes are (we believe) efficient
quantum information processors.
How long do we have to wait for
information absorbed by a black hole
black
to be revealed in its emitted Hawking
hole
radiation? We have recently
reconsidered this question using
maximal
Alice’s
new tools from quantum information
entanglement
qubits
theory.
Our (tentative) conclusion is that the retention time can be surprisingly short.
The analysis uses the theory of quantum error-correcting codes and quantum
circuits.
Quantum Information Science
Atomic-Molecular
Optical Physics
Exotic Quantum
States of Matter!
Condensed
Matter Physics
Preskill
Kimble
Painter
Vahala
Kitaev
Schulman
Eisenstein Roukes Refael
Motrunich
Exotic Quantum
States of Matter!
All-Star
All-Star