From Atoms to Quantum Computers: the classical and quantum faces of nature Antonio H. Castro Neto...
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![Page 1: From Atoms to Quantum Computers: the classical and quantum faces of nature Antonio H. Castro Neto Dartmouth College, November 2003.](https://reader036.fdocuments.in/reader036/viewer/2022062714/56649d635503460f94a45c7f/html5/thumbnails/1.jpg)
From Atoms to Quantum Computers: the classical and
quantum faces of nature
Antonio H. Castro Neto
Dartmouth College, November 2003
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Newton’s equation: m dx = F d t
2
2
Isaac Newton
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Particles
Waves
Continuous andDeterministicUniverse
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Erwin Schrödinger
Quantum mechanics:A discrete and probabilisticUniverse
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i h dd t
1 2
1 2
1 2 2 1
2 2 2
* *
Interference
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UP DOWN
LINEAR SUPERPOSITION
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Where do Classical and Quantum Mechanics meet?Schrödinger's cat
Life) + (Death)(Life)
(Death)
Wavefunction Collapse
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Schrödinger's cat: molecular magnets
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Two-Level System
ClassicalParticle
QuantumParticle
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<x(t)>
Harmonic Oscillator
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Courtesy of P.Mohanty BU
Ultra smallOscillators:Nanowires
Width ~ 10 human hair -6
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Dissipation
Couplingto theenvironment
Damped Harmonic Oscillator
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DecoherenceUniverse: system of interest + environment
System of interest: and
Environment: n,m=
Decoupled at t=0:
After a time t= :
1 2
n n m
U 1 2 n
U 1 2 1 2 2 1
2 2 2 * *
D U 1 n 2 m
U 1 2 1 2 n m 1 2 m n
2 2 2 * *Classical Result !
eD 0
-N
Pure State
Mixture
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Jun Kondo
Electron movingin a crystal with Magnetic impurities
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Kondo effect
Spin Flip
MultipleSpin flips
<S >z
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Don EiglerIBM
ScanningTunnelingMicroscope
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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 √x → 2N/2 =eN ln(2)/2
Quantum Computer: probabilistic and non-sequential
Basis states: x0 ,x1 ,x2 ,…xN)Arbitrary state: yi}) = ∑{xi}
c{xi}({yi}) xi})
Probability: | c{xi}({yi}) |2
Shor’s 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 thequbits interact and have littledecoherence?
Use of low dimensionalmaterials – E. Novais,AHCN cond-mat
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Quantum Frustration AHCN, E.Novais,L.Borda,G.Zarandand I. Affleck PRL 91, 096401 (2003)
Environment withlarge spin (classical)
S=½
The energy is dissipated into two channelscoupled to Sx and Sy . However: [Sx ,Sy ] = i ћ 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.