From Atoms to Quantum Computers: the classical and quantum faces of nature

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From Atoms to Quantum Computers the classical
and quantum faces of nature

• Antonio H. Castro Neto
• Dartmouth College, November 2003

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Newtons equation m dx F d t
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Isaac Newton
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Particles
Waves
Continuous and Deterministic Universe
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Quantum mechanics A discrete and
probabilistic Universe
Erwin Schrödinger
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i h dY H Y d t
Y Y Y
1 2
2 2 2
Y Y Y Y Y Y Y
1 2

1 2 2 1
Interference
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UP
DOWN
LINEAR SUPERPOSITION
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Where do Classical and Quantum Mechanics meet?
Schrödinger's cat
Y(Life)
Y Y(Life) Y(Death)
Wavefunction Collapse
Y(Death)
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Schrödinger's cat molecular magnets
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Two-Level System
Classical Particle
Quantum Particle
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ltx(t)gt
Harmonic Oscillator
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Ultra small Oscillators Nanowires
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Width 10 human hair
Courtesy of P.Mohanty BU
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Dissipation
Coupling to the environment
Damped Harmonic Oscillator
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Decoherence
Universe system of interest environment System
of interest y and y Environment F , lt F
F gt 0 n,m1,2,3... Decoupled at t0
Y (y y ) F Y y y
y y y y After a time tt Y y F Y F
Y y y y y ltF F gt y y ltF F gt
1 2
n n m
Pure State
U 1 2 n
-N
2 2 2

t t e
D 0
U 1 2 1 2
2 1
Mixture
D U 1 n 2 m
2 2 2

Classical Result !
U 1 2 1 2
n m 1 2 m n
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Jun Kondo
Electron moving in a crystal with Magnetic
impurities
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Kondo effect
Spin Flip
Multiple Spin flips
ltS gt
z
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Don Eigler IBM
Scanning Tunneling Microscope
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Quantum Computation
Classical Computer deterministic and
sequential Factorization of x x0 20 x1 21
. (x0 ,x1 ,x2 ,xN) Solution Try all primes
from 2 to vx ? 2N/2 eN ln(2)/2 Quantum
Computer probabilistic and non-sequential Basis
states y(x0 ,x1 ,x2 ,xN) Arbitrary state
Y(yi) ?xi cxi(yi) y(xi) Probability
cxi(yi) 2 Shors algorithm N3
Exponential explosion!
Power law growth
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Solid State Quantum Computers
_Scalable large number of qubits _States can be
initiated with magnetic fields _Quantum gates
qubits must interact _Qubit specific acess
Big challenge How to make the qubits interact
and have little decoherence?
Use of low dimensional materials E.
Novais, AHCN cond-mat
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Quantum Frustration
AHCN, E.Novais,L.Borda,G.Zarand and I. Affleck
PRL 91, 096401 (2003)
Environment with large spin (classical)
S½
The energy is dissipated into two
channels coupled to Sx and Sy . However
Sx ,Sy i ? Sz
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Conclusions
_There is a lot of room at the bottom
R.Feynman _There is a lot of beauty
and basic phenomena. _ Experiments are probing
the boarders between classical and quantum
realities and also the frontiers of
technology. _ New theoretical approaches and
ideas are required.