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2010 Michigan Quantum Summer SchoolQuantum Simulation and Metrology
August 2 – 13, 2010
http://www.umich.edu/~mctp/SciPrgPgs/events/2010/MQSS10/index.html
Aaron Leanhardt Hui Deng Luming Duan Chris Monroe Angela Milliken
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Michigan Summer Symposia: 1928-1941
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Michigan Summer Symposia: 2008-
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QuantumMechanics
InformationTheory
Quantum Information Science
A new science for the 21st Century?
20th Century
21st Century
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JOINTQUANTUMINSTITUTE
Quantum Simulations
ChrisMonroe University of Maryland
Department of PhysicsNational Institute ofStandards and Technology
with Ions
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Quantum science for tomorrow’s technology
JOINTQUANTUMINSTITUTE
http://www.lps.umd.edu/index.html�
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Quantum Simulation: What is it?
Ψ=Ψ Hdt
diΨ Describes N interacting systems, each system having D degrees of freedom
DN coupled differential equations
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Ψ=Ψ H
dtdi
PhysicalSystem
Ψ
TrialH
Ψ=Ψ H
dtdi
PhysicalSystem
Ψ
ChooseH
Two approaches
(1)
(2)
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Quantum Computing:parallel processing on 2N inputs
Example: N=3 qubits
Ψ = a0 |000〉 + a1|001〉 + a2 |010〉 + a3 |011〉a4 |100〉 + a5|101〉 + a6 |110〉 + a7 |111〉
f(x)
Measurement gives random result
e.g., Ψ⇒ |101〉 f(x)
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depends on allinputs
quantumlogic gates
quantum interference saves the day!
Deutsch (1985)Shor (1994)Grover (1996)
fast number factoring N = p×qfast database search
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depends on allinputs
quantumlogic gates
|0〉 |0〉 → |0〉 |0〉|0〉 |1〉 → |0〉 |1〉|1〉 |0〉 → |1〉 |1〉|1〉 |1〉 → |1〉 |0〉
e.g., |0〉 + |1〉 |0〉 → |0〉|0〉 + |1〉|1〉quantumXOR gate:
superposition → entanglement
|0〉 → |0〉 + |1〉|1〉 → |1〉 − |0〉
quantum√NOT gate:
( )
quantum interference saves the day!
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from S. Lloyd, Science 319, 1209 (2008)
Quantum simulations with individual atoms
D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901 (2004)X.-L. Deng, D. Porras, and J. I. Cirac, Phys. Rev. A 72, 063407 (2005)A. Friedenauer, et al., Nature Physics 4, 757 (2008)K. Kim, et al., Phys. Rev. Lett. 103, 120502 (2009)K. Kim, et al., Nature 465, 590 (2010)E. Edwards, et al., Phys. Rev. B (2010); ArXiv 1005.4160
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Yb+ crystal
~5 µmMunichOxfordParisSiegenSeattle (UW)Simon FraserSussexTokyoUlmWeizmann Inst.
BarcelonaBerkeleyBoulder (NIST)DukeGeorgia TechGriffith (Australia)InnsbruckLos AlamosMaryland/JQIMIT
C.M. & D. J. Wineland, Sci. Am., 64 (Aug 2008)R. Blatt & D. J. Wineland, Nature 453, 1008 (2008)
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Trapped Atomic Ions
spin-dependent force
F = F0|↑〉〈↑| − F0|↓〉〈↓|
Slow: Coulomb-coupled nonlocal normal modes, phonons
~5 µm↑
↓
↑
↓d
δ
...2
)(3
22
22
22
+−=+
=d
ede
de
se δ
δ
δ ~ 20 nme δ ~ 1000 Debye
Fast: dipole-dipole coupling (or other forms)
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F = F0|↑〉〈↑| − F0|↓〉〈↓|
Global spin-dependent force
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↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↓↑ ↓↑ ↓↑ ↓↓↑↓ ↑↓ ↑
↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↓↑ ↓↑ ↓↑ ↓↓↑↓ ↑↓ ↑
F = F0|↑〉〈↑| − F0|↓〉〈↓|
Global spin-dependent force|↑〉
|↓〉
ADD: Independent spin flips
B
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Figure from Porras and CiracPRL 92, 207901 (2004)
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171Yb+ hyperfine qubit
2S1/2(3 kHz/G @ 5 G)
νHF = 12,642,812,118 + 311B2 Hz
|↓〉 = |0,0〉
|↑〉 = |1,0〉
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