Download Quantum Computing with Atoms in Optical Nanostructures

National Institute of Standards and Technology
Quantum Information Program
“Quantum Computing with Atoms in
Optical Nanostructures”
William D. Phillips
Laser cooling and trapping group
National Institute of Standards and Technology
Gaithersburg MD 20899-8424
[email protected]
NNI Interagency Workshop
Instrumentation and Metrology for Nanotechnology
Grand Challenge Workshop
27-29 January 2004 Gaithersburg MD
Sponsors:
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Two Questions:
What is quantum computing?
What does it have to do with Nanotechnology?
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Two Questions:
What is quantum computing?
A: An entirely new paradigm for information
processing, with astounding potential for
improved speed of calculation.
What does it have to do with Nanotechnology?
A: Almost everything
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A quantum computer would
be more different from
today’s digital computers
than today’s computers are
from the abacus.
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Today, a wide variety of government agencies,
industrial and commercial concerns are heavily
invested in the study of quantum information.
Why all the interest?
•Quantum computers, if made, could solve problems that are
impossible to solve with ordinary, classical computers.
•Quantum processing allows measurements to be made at the
limits set by quantum mechanics--huge potential
improvements.
•Quantum communication offers security against
eavesdropping, guaranteed by the laws of physics.
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The “Killer App.”
Factoring numbers is a difficult problem--the time
required grows exponentially with the digits in the
number to be factored.
The difficulty (impossibility) of factoring large numbers (and the ease of
creating a large number from its factors) is the basis of public key
encryption (which nearly everyone uses for secure transmission today).
A quantum computer would be able to use
Shor’s Algorithm to factor numbers in a time
growing only as a power of the number of digits.
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Quantum information has captured the imagination of
people ranging from physicists to science fiction writers!
“Using Shor’s quantum factorization
algorithm, one can see that factoring a
large number can be done by a QC –
quantum computer – in a very small
fraction of the time the same number
would take using ordinary hardware. A
problem that a SuperCray might labor
over for a few million years can be
done in seconds by my QC. So for a
practical matter like code breaking, the
QC is vastly superior.”
…
“Wineland and Monroe worked out
the single quantum gate by trapping
beryllium ions. …”
----Clancy and Piecznik
N.B: Wineland and Monroe, at NIST-Boulder
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But Quantum Information/Computation is NOT
science fiction and there is lots of active research at
NIST, throughout the US and around the world.
Why?
•There are lots of important applications.
•The issues of quantum information go to the heart of the most
mysterious and fundamental aspects of physics.
•The known computation power for interesting problems is
astounding: factoring and other Shor-algorithm-like problems
have a different complexity class!
•Quantum computers might be able to solve GENERAL hard
problems. The implications are mind boggling!!
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Implications of general solutions of “hard” problems
“Setting aside the constraints of any particular computational
model, the creation of a physical device capable of brutally solving
NP problems would have the broadest consequences. Among its
minor applications it would supercede intelligent, even artificially
intelligent, proof finding with an omniscience not possessing or
needing understanding. Whether such a device is possible or even in
principle consistent with physical law, is a great problem for the next
century.”
Michael H. Freedman (Fields Medalist)
Microsoft Corporation
Source: “Topological Views on Computations Complexity,” Documenta
Mathematica, Extra Volume ICM 1998, II, 453-464
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Classical Bits vs Quantum Bits
Classical Bit: 0 or 1;  or 
Quantum Bit (Qubit):
Can be a quantum superposition of 0 and 1
y
1
=
qubit

1
+
1
Superposition is one of the two weirdest
things about Quantum Mechanics;
Entanglement is the other.
It is what gives quantum computing its power!
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The Einstein-Poldoski-Rosen “Paradox”
Before you measure, the spins
could have either direction.
?
?
|
>|> - |>|>
When you measure, the spins they
are always anticorrelated--entangled,
in a way impossible if the spins’
values existed before measurement-a weirdness that spooked Einstein
20th Century quantum technology doesn’t generally use the
weirdness of quantum mechanics. Quantum information technology
DOES--a second quantum revolution!!
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Scaling is the key to the power of Qu. Information.
• Classically, information is stored in a bit register: a 3-bit
1 0 1
register can store one number, from 0 – 7.
• Quantum Mechanically, a register of 3 entangled qubits can
store all of these numbers in superposition:
a|000 + b|001 + c|010 + d|011  + e|100 + f|101 + g|110  + h|111 
• Result:
-- Classical: one N-bit number
-- Quantum: 2N (all possible) N-bit numbers
•N.B.: A 300- qubit register can simultaneously store
more combinations than there are particles in the universe.
Problems in both cryptography and physics benefit from this
exponential scaling, enabling solutions of otherwise
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insoluble problems.
Another “Killer App.”
We live in a quantum world, but we try to model
its behavior with classical computers.
Classical computers are inadequate, because the size
of the problem grows exponentially with the size of
the physical system. Quantum computers work the
problem as nature would. Richard Feynman’s
recognition of this fact started modern interest in
quantum information.
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A Killer Metrology Application
(e.g., spin-squeezing in Wineland’s group)
The nature of uncertainty is of
primary concern in accurate
measurement
N classical,
independent
atoms
measurement
uncertainty
1

N
shot-noise limit
N quantum-entangled atoms
1

N
Heisenberg limit
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One more killer app. -- Quantum Communication
 1  2   1
Quantum
Repeater
2
?
Alice
?1
1
Eve can only obtain
information by
destroying the qubits
(no-cloning theorem)
2
?
2
Bob
Eve
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A New Science!
Quantum
Mechanics
20th Century
Information
Science
The second
quantum
technology
revolution
Quantum Information Science
21st Century
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Real Qubits
What is a qubit, physically?
It must be, in some sense, small enough to be
quantum mechanical (which is why QI is usually nanoscale)
Some examples:
 Photons (N. B. NIST QKD testbed)
 Quantum Dots
 Single Cooper-Pair Boxes
 Josephson-Junction Circuits (N. B. Martinis’s program)
 Nuclear spins in liquids
 Electron/nuclear spins in solids
 Single Isolated Ions (N. B. Wineland’s program)
 Single Isolated Atoms
 Etc.
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(Simplified) Atomic Qubit
An atom with nuclear and electron spins
higher energy state: 1
lower energy state:
An atom can be 1
1 , or it can be 0 ,
but it can also be
00
01 
+ 1
0
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Atom-Light Interaction &
Traps
Optical lattice holds, manipulates atoms by light shift
Light shift
e
Counter-propagating laser beams
D
2
hn  ~ I
g
2
4D
create a standing wave. Periodic
light-shift potential = optical lattice
Photon scattering (decoherence) ~ 2/D2
so decoherence can be made small
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The periodic potential of an optical
lattice is a natural, nanoscale
register for atomic qubits
w
w
~400 nm
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Loading a BEC into a Lattice
Bose-Einstein Condensate:
Huge number of atoms in lowest
state in a magnetic trap
Bose-Einstein Condensation + Optical Lattice
Adiabatic turn-on: All of
the BEC in the lowest
state.
Non-adiabatic:
superposition of excited
states.
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Measuring the loading of a lattice
Suddenly (non-adiabatically) releasing the atoms from the
lattice projects the lattice wavefunction into free space.
The periodic wavefunction has momentum components at
multiples of the reciprocal lattice momentum-- twice the
photon momentum (2nk).
(This is the same as diffraction!)
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Temporal Evolution of Loaded, 1-D Lattice
Adiabatic
Non-adiabatic
Adiabatic loading puts atoms > 99.5% in the ground state.
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But, we also need to have just one atom per site!
Mott transition: initialization of >105 qubits in a 3-d lattice
Mott
Lattice is deepened adiabatically;
repulsive interactions arrange
atoms, one per site.
Phil. Trans. R. Soc. Lond. A 361, 1417 (2003)
Lattice
Depth
BEC
200 ms
(similar results in Munich)
According to theory, ground state provides a very high fidelity
initialization of a massive register of neutral atom qubits (at
V0= 35 ER, < 5% chance of any of 105 sites having an error). 24
Quantum Processing: single bit
operations
(excited state)
w1

Raman transitions:
two laser beams
induce transitions
between the atomic
qubit states.
w2

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A problem: atoms in adjacent lattice
sites are not optically resolved
tightly focused laser
beam hits more than
one atom
We want tightly confined
atoms, far enough apart
to resolve with a laser.
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Our approach: Use a superlattice to
localize atoms into every nth lattice site
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Patterned loading
x
NIST-Gaithersburg 2002
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Quantum Processing: 2-bit gate operations
2-bit, neutral-atom universal gates work by entangling atomic states
through coherent atom-atom collisions.
A simple approach is the CiracZoller gate in which stateselective movement of atoms and
ground-state, on-site interaction
between atoms accomplishes the
entanglement:
atom 1
atom 2
Preliminary results
on controlled
coherent phase
shift in Munich
move
s+

s
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Where we stand in quantum computation with
neutral atoms in optical nanostructures:
• The needed tools (qubits, gates, readout, …) have
all been demonstrated in principle.
• We need to do operations at the single atom level
(nanoscale manipulation and detection).
• We need high fidelity of operations--nanoscale
metrology
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Conclusions
When will we have a quantum computer?
A small-scale processor (~ 10 qubits), capable of acting as a quantum
repeater, should be available within the decade.
A larger scale computer that can factor large numbers will be very
difficult, but no fundamental roadblocks have appeared. It will
probably take more than 20 years.
Quantum information/engineering is a already a reality:
Prototype quantum communication systems are operating in several
locations (including NIST).
Processors that can simulate important condensed matter problems at
the nanoscale are on the horizon.
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