Transcript Preskill-PMAChairsCouncil7dec2009

CEQS
CENTER FOR EXOTIC QUANTUM SYSTEMS
1983
2002
2005
2006
2009
Preskill
Kitaev
Refael
Motrunich
Fisher
Historically, Caltech physics has focused on the most “fundamental” problems,
such as the structure of matter at the smallest conceivable scales, and the
structure of the universe at the largest conceivable scales. These problems
are still enormously exciting, but there is also another frontier, just as exciting
and important, which might be called the “entanglement frontier.”
Research in this area aims to understand and exploit the exotic and baffling
correlations exhibited by quantum systems. State-of-the-art experiments can
be done on a tabletop, and there are very strong ties between experiment and
theory.
CEQS
CENTER FOR EXOTIC QUANTUM SYSTEMS
1983
2002
2005
2006
2009
Preskill
Kitaev
Refael
Motrunich
Fisher
In the 21st century, building strength in quantum many-body theory has been a
high priority for Caltech physics, and we have been quite successful.
Furthermore, links to the theory of computation and to atomic-molecularoptical physics make this research highly interdisciplinary, something Caltech
does especially well.
A central theme: seeking new paradigms for describing universal emergent
phenomena in quantum systems containing many particles. We need new
ideas to erect a “grand unified theory” of exotic quantum systems!
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 (highly entangled)
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.
That’s why highly correlated
quantum systems can behave in
ways that we find hard to
understand.
But it also means that controlling
highly entangled systems might be
very powerful. As Feynman first
suggested in 1981, a computer that
operates on qubits rather than bits
(a quantum computer) should be
able to perform tasks that are
beyond the capability of any
conceivable digital computer!
Decoherence
1
2
(
+
Environment
)
Decoherence
1
2
(
+
)
Environment
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.
Quantum
Computer
Decoherence
ERROR!
Environment
How can we protect a
quantum system from
decoherence and other
sources of error?
CEQS
CENTER FOR EXOTIC QUANTUM SYSTEMS
Why Fellowships?
In theory as in experiment, students and postdocs make an essential
contribution to the research effort. That’s particularly true when it comes to
exploiting interdisciplinary opportunities and fast-breaking developments.
Students and postdocs can provide the glue that binds different research
groups together, and often they lead the faculty into new territory rather
than the other way around.
Gottesman:
Quantum errorcorrecting codes
Bacon:
Selfcorrecting
systems
Smith:
Quantum
channel
capacities
Bonderson:
Experimental
signature of
nonabelian
statistics.
Verstraete:
Complexity of
quantum
problems
Chang:
Entangling
mechanical
oscillators
Efficient classical simulation of quantum
systems with bounded entanglement
Vidal
In general, there is no succinct classical description of the quantum state
of a system of n qubits. But suppose, e.g., for qubits arranged in one
dimension, that for any way of dividing the line into two segments, the
strength of the quantum correlation (the amount of entanglement)
between the two parts is bounded above by a constant, independent of n.
Vidal showed that in that case a succinct description is possible, with O(n)
parameters rather than 2n, and that the description can be easily updated
as the state evolves (if the interactions are local).
This makes precise the idea that entanglement is the source of a quantum
computer’s power: if the quantum computer does not become highly
entangled, it can be efficiently simulated by a classical computer.
Furthermore, in one-dimensional systems with local interactions, the
entanglement increases no more rapidly than log n, and an efficient
classical simulation of real time evolution is possible.
Universal properties of entanglement
For the ground state of a large two-dimensional quantum
system, consider the entanglement of a disk
(circumference L) with the rest of the system. For a
system with a nonzero energy gap, the entanglement is:
Kitaev
Preskill
E L  
Term proportional to L, arising from
short distance fluctuations near the
boundary, is nonuniversal.
Additive correction is universal
(independent of geometry and
microscopic details).
The universal additive term, the topological
entanglement entropy, is a global feature of the
many-body quantum entanglement, characterizing
the topological order of the gapped two-dimensional
system. There is a simple formula for the universal
constant , in terms of the properties of the particle
excitations of the system.
L
Quantum Information Science
Atomic-Molecular
Optical Physics
Condensed
Matter Physics
CEQS!