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“Quantum Computing with Atoms in Optical Nanostructures”

William D. PhillipsLaser cooling and trapping group

National Institute of Standards and TechnologyGaithersburg MD 20899-8424

william.phillips@nist.gov

NNI Interagency WorkshopInstrumentation and Metrology for Nanotechnology

Grand Challenge Workshop27-29 January 2004 Gaithersburg MD

Sponsors:

National Institute of Standards and TechnologyQuantum Information Program

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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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“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

Quantum information has captured the imagination of people ranging from physicists to science fiction writers!

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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“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

Implications of general solutions of “hard” problems

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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

1 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!

qubit

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The Einstein-Poldoski-Rosen “Paradox”

??

| > | > - | > | >

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!!

Before you measure, the spins could have either direction.

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Scaling is the key to the power of Qu. Information.

• Classically, information is stored in a bit register: a 3-bitregister can store one number, from 0 – 7.

•

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 storemore combinations than there are particles in the universe.

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Problems in both cryptography and physics benefit from this exponential scaling, enabling solutions of otherwise

insoluble problems.

Quantum Mechanically, a register of 3 entangled qubits can store all of these numbers in superposition:

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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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The nature of uncertainty is of primary concern in accurate measurement

N classical,independent

atoms

N quantum-entangled atoms

measurementuncertainty

shot-noise limit

Heisenberg limit

N

1

N

1

A Killer Metrology Application(e.g., spin-squeezing in Wineland’s group)

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EveEve can only obtain

information by destroying the qubits(no-cloning theorem)

Alice

1

2

1

2

2?

2?

QuantumRepeater

Bob1??

1

One more killer app. -- Quantum Communication

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A New Science!

QuantumMechanics

InformationScience

Quantum Information Science

20th Century

21st Century

The secondquantum technology revolution

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Real Qubits

What is a qubit, physically?

It must be, in some sense, small enough to bequantum 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: 0

An atom can be , or it can be ,

but it can also be

010 1

2

1

0

1 01 0

2

+

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Atom-Light Interaction & Traps

Optical lattice holds, manipulates atoms by light shift

e

hg

2

4

Light shift

2 ~ I

Counter-propagating laser beams

create a standing wave. Periodic light-shift potential = optical lattice

Photon scattering (decoherence) ~

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

~400 nm

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Loading a BEC into a Lattice

Adiabatic turn-on: All of the BEC in the lowest state.

Non-adiabatic: superposition of excited states.

Bose-Einstein Condensation + Optical Lattice

Bose-Einstein Condensate:Huge number of atoms in lowest state in a magnetic trap

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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 (2nk).

(This is the same as diffraction!)

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Temporal Evolution of Loaded, 1-D Lattice

Non-adiabatic

Adiabatic

time

Adiabatic loading puts atoms > 99.5% in the ground state.

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Mott transition: initialization of >105 qubits in a 3-d lattice

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).

BEC

Mott

Latti

ce

Dep

th

200 ms

Phil. Trans. R. Soc. Lond. A 361, 1417 (2003)

Lattice is deepened adiabatically; repulsive interactions arrange atoms, one per site.

But, we also need to have just one atom per site!

(similar results in Munich)

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Quantum Processing: single bit operations

Raman transitions: two laser beams induce transitions between the atomic qubit states.

(excited state)

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A problem: atoms in adjacent lattice sites are not optically resolved

tightly focused laserbeam hits more than one atom

We want tightly confinedatoms, far enough apartto 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

p

NIST-Gaithersburg 2002

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Quantum Processing: 2-bit gate operations2-bit, neutral-atom universal gates work by entangling atomic states through coherent atom-atom collisions.

A simple approach is the Cirac-Zoller gate in which state-selective movement of atoms and ground-state, on-site interaction between atoms accomplishes the entanglement:

move

atom 1 atom 2

+ -

Preliminary results on controlled coherent phase shift in Munich

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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.