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

Michigan Summer Symposia: 1928-1941

Michigan Summer Symposia: 2008-

QuantumMechanics

InformationTheory

Quantum Information Science

A new science for the 21st Century?

20th Century

21st Century

JOINTQUANTUMINSTITUTE

Quantum Simulations

ChrisMonroe University of Maryland

Department of PhysicsNational Institute ofStandards and Technology

with Ions

Quantum science for tomorrow’s technology

JOINTQUANTUMINSTITUTE

http://www.lps.umd.edu/index.html�

Quantum Simulation: What is it?

Ψ=Ψ Hdt

diΨ Describes N interacting systems, each system having D degrees of freedom

DN coupled differential equations

Ψ=Ψ H

dtdi

PhysicalSystem

Ψ

TrialH

Ψ=Ψ H

dtdi

PhysicalSystem

Ψ

ChooseH

Two approaches

(1)

(2)

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)

depends on allinputs

quantumlogic gates

quantum interference saves the day!

Deutsch (1985)Shor (1994)Grover (1996)

fast number factoring N = p×qfast database search

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!

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

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)

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)

F = F0|↑〉〈↑| − F0|↓〉〈↓|

Global spin-dependent force

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↓↑ ↓↑ ↓↑ ↓↓↑↓ ↑↓ ↑

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↓↑ ↓↑ ↓↑ ↓↓↑↓ ↑↓ ↑

F = F0|↑〉〈↑| − F0|↓〉〈↓|

Global spin-dependent force|↑〉

|↓〉

ADD: Independent spin flips

B

Figure from Porras and CiracPRL 92, 207901 (2004)

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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