Quantum Simulator

A poor man’s quantum computer? more than one quantum simulator?

(a)addressing different questions (b)addressing identical questions

quantum simulatorby different systems?testing the “non-testable” = universal quantum computer

ions: +large interaction strength (kHz not Hz) @ small decoherence rates … +outstanding initialization /preparation however1: -scalability -intrinsically (+bosons/ -fermions) however2: +dream to combine advantages Didi’s

NJP-special issue on quantum simulations (04.2011) Tillman Esslinger, Chris Monroe, Tobias Schaetz outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î example for QS (quantum walk, quantum magnet) Î similarities/differences between QS and QC

after successful exp. proof of principle vision Î outperform classical computation Î deeper insight in complex quantum dynamics suggesting 3 objectives - #1: decoherence = error - #2: scaling radio-frequency (Penning) traps + minimizing effort - #3: new prospects: ions (and atoms) in optical lattices different classes of quantum simulations class 1 class 2 explore new physics in the laboratory outperform classical computation (perhaps even trackable classically) address the classically simulating analogues: non-trackabkle nonlinear interferometers D. Leibfried, DJ.Wineland et al. PRL (2002)

L.Lamata, E.Solano,T.Schaetz et al. PRL (2007) Dirac equation R.Blatt’s group Nature (2010) +Klein paradox R.Blatt’s group PRL (2011) H.Landa, A.Retzker, B.Reznik et al. PRL (2010) Solitons Milburn PRL 2005 R.Schuetzhold, T.Schaetz et al. PRL (2007) early universe Milburn PRA 2002 H.Schmitz, Ch.Schneider, T.Schaetz et al. PRL (2009)

(quantum walks) C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) (Duffing oscillator-Roee) R.Ozeri et al., arXiv (2010)

Frenkel Kontorova model Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it Blatt group (2010)

Kibble-Zureck mechanism W.H.Zurek, P.Zoller et al. PRL (2005) different classes of quantum simulations class 1 class 2 explore new physics in the laboratory outperform classical computation (perhaps even trackable classically) address the classically simulating analogues: non-trackabkle nonlinear interferometers D. Leibfried, DJ.Wineland et al. PRL (2002)

L.Lamata, T.Schaetz et al. PRL (2007) Dirac equation R.Blatt’s group Nature (2010) + HT on Klein paradox H.Landa, A.Retzker, B.Reznik et al. PRL (2010) Solitons

Milburn PRL 2005 early universe R.Schuetzhold, T.Schaetz et al. PRL (2007) Milburn PRA 2002 (quantum walks) Ch.Schneider, T.Schaetz et al. PRL (2009) + Poster #39 C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010) (Duffing oscillator-Roee) R.Ozeri et al., arXiv (2010)

MPQ (2010) Frenkel Kontorova model Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it

L.Lamata, E.Solano,T.Schaetz et al. PRL (2007) Dirac equation R.Blatt’s group Nature (2010)

H.Landa, A.Retzker, B.Reznik et al. PRL (2010) Solitons

Milburn PRL 2005 early universe R.Schuetzhold, T.Schaetz et al. PRL (2007)

Milburn PRA 2002 (quantum walks) Ch.Schneider, T.Schaetz et al. PRL (2009) C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010)

(Duffing oscillator-Roee) R.Ozeri et al., arXiv (2010)

Frenkel Kontorova model Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it

Kibble-Zureck mechanism W.H.Zurek, P.Zoller et al. PRL (2005) quantum walk

(1) qubit = coin (2) one qubit gate = coin-flip (3) conditional gate = step coin – operation: step – operation: x p quantum walk: results (position space)

0.633± 0.012 [PRL (2009)]

0.121± 0.007 see also: C.Roos et al. Innsbruck [PRL (2009)] different classes of quantum simulations class 1 class 2 explore new physics in the laboratory outperform classical computation (perhaps even trackable classically) address the classically simulating analogues: non-trackabkle nonlinear interferometers D. Leibfried, DJ.Wineland et al. PRL (2002)

L.Lamata, E.Solano,T.Schaetz et al. PRL (2007) Dirac equation R.Blatt’s group Nature (2010)

H.Landa, A.Retzker, B.Reznik et al. PRL (2010) Solitons

Milburn PRL 2005 early universe R.Schuetzhold, T.Schaetz et al. PRL (2007)

Milburn PRA 2002 (quantum walks) Ch.Schneider, T.Schaetz et al. PRL (2009) C.Sanders, D.Leibfried et al. PRL (2009) R.Blatt’s group PRL (2010)

(Duffing oscillator-Roee) R.Ozeri et al., arXiv (2010)

Frenkel Kontorova model Garcia-Mata et al., Eur. Phys. J. D (2007) + H.Haeffner working on it

Dirac equation D.Porras and I.Cirac PRL (2004) Bose-Hubbard model

Solitons D.Porras, I.Cirac et al. PRA (2008) Spin boson model early universe quantum spin Hamiltonians D.Porras and I.Cirac PRL (2004) (quantum walks) Schaetz’s group Nature Physics (2008) (e.g. quantum Ising Monroe’s group Nature (2010) spin frustration)

(Duffing oscillator-Roee) Anderson localization D.Porras three particle interaction Frenkel Kontorova model see also Bollinger et al. (+ Thompson & Segal et al.) Kibble-Zureck mechanism beautiful work in Penning traps – Nature 2009 outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î play through one example for QS (quantum magnet) Î discuss differences between QS and QC

(1) qubit = spin (σ) (2) one qubit gate = spin-flip (B-field) (3) two qubit gate = spin-spin (J)

spin-flip (B-field): x xzzspin-spin (J): HB=− ∑σ ii+J∑σσj ii, j quantum Ising model

P x xx yyyXY model HJ=+∑σi σσσj J∑ i j ij,,ij

x xx yyyzzzHeisenberg pulse HJduration=++σ σσσσσ J J ∑∑∑i j i j i j model ij,,,ij ij quantum magnet

xx zz HB=− ∑σ ii+J∑σσj ii, j amplitude adiabatic evolution+ n<0.03 J(t)

B duration prepare initialize simulate (analyse) detect

ground state ground state

Bxxσ zz ∑ i x J∑σijσ i |/JB|=1 i, j summary: what’s up spins? xx zz HB=−∑σ iij + J∑σσ ii, j Jmax Bx adiabatic transition: fidelity( v ) J

B =|J(t)| x +

98%+- 2% J z z −+Bxx()σ σ x Jσ σ 12 12 simulating a quantum magnet in an ion trap outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î play through one example for QS (quantum magnet) Î discuss differences between QS and QC

-stroboscopic pulses (!t!) -continuous evolution (J and B) -non equilibrium (oscillation) -equilibrium (adiabatic) -error correction (e.g. spin echo) -robust (inherent correction) -decoherence = error -decoherence = ?nature? -1.1 dimensional trap network -2 dimensional trap-lattice outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î play through one example for QS (quantum magnet) Î discuss differences between QS and QC

Îrobust: reduced impact of decoherence (e.g. quantum phase transitions?) ?+?

Îgadget: engineered decoherence (e.g. simulate “natural” noise?)

Înecessary: enhanced (quantum) efficiency by decoherence (e.g. in biological systems?) outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î play through one example for QS (quantum magnet) Î discuss differences between QS and QC

cross section

? top view ?

Îextend into second dimension (arrays of ions)

Îoptimize architecture for quantum simulations (no cryogenics, large Jspin/spin) Î(potentially without lasers) trapology –theory - scaling

quadratic lattice Schmied,Wesenberg, Leibfried PRL(2009)

triangular lattice – collaboration: R.Schmied, NIST, Sandia ion trapper’s perspective

main challenge: Jan 2011: trapping ions scaling to many ions/spins 2010: optically trapping an ion in SANDIA’S surface trap +ion trapped in 1D optical lattice

Îions in 2D rf-surface traps Îions (atoms) in optical lattices outline: experimental Quantum Simulations (QS)

Î different implementations of QS (luxury?) Î different classes (intentions) of QS +incomplete list of examples

Î play through one example for QS (quantum magnet) Î discuss differences between QS and QC

sharing advantages of ions and optical lattices: for 60 years: for 30 years: ions in radio frequency fields atoms in optical fields

Îindividual addressability

Îoperations of high fidelity (>99%) + arrays of traps Îlong range interaction (Jspin/spin>20kHz) I.Bloch should not compete but complete

first step in our lab: trapping an ion in optical dipole trap* Î lifetime limited by -loading and cooling in rf-trap recoil heating only -dipole trap on / rf-trap off Î several 100s of oscillations in optical potential Î loading via rf-trap without heating Îion trapped in optical lattice - detection in rf-trap *Nature Photonics (2010) optical dreaming scaling quantum simulations with ions (atoms) in an optical lattice ( ) trapping and cooling ion(s) in (hybrid) optical lattice atoms and ions in common 1D optical lattice*1 (e.g. electron tunnling)

Îions/spins in 2D/3D optical lattice*1 (old QS) n o si vi Îatoms and ion(s) in common 2D/3D optical lattice*1 (new QS) *1priv. com. I.Cirac and P.Zoller

Îatom and ion in common optical trap (no micromotion) ( ) ion separation universal quantum computing ( ) pushing gate*2 for ions in optical trap array

+ hybrid (Coulomb crystal in RF + optical lattice*2) *2Nature: Cirac,Zoller (2010) *3NJP: Cirac group (2008) summary: novel physics

#1 #2 #3

decoherence = error scaling quantum simulations in ion traps

Îproof of principle on ions (and atoms) for Îhow to mitigate, quantum simulations how to exploit it bridging the gap (chemistry/biology) (proof of principle studies and “useful” QS) Î outperforming classical computation Îhow to investigate Î deeper understanding of quantum dynamics (10x10 spins) (mesoscopic) decoherence

investigate the impact on:

- solid state physics (magnets, ferroelectrics, quantum Hall, high Tc) (quantum phase transitions, spin frustration, spin glasses,…) - quantum information processing / quantum metrology - cold chemistry (cold collisions) -…

Max-Planck Institute for Quantum Optics Garching Deutsche Forschungsgemeinschaft

IMPRS-APS

+ Taro PhDs: (Hector Schmitz) (Axel Friedenauer) TIAMO ChristianQSim Schneider Trapped IonsPhDs: And MOlecules Quantum Simulations Steffen Kahra Martin Enderlein newsGünther from Leschhorn the miacGS: GS: Thomas Huber Tai Dou (Robert Matjeschk) 3.8 fs beam line post (Jandoc Glückert) position (Lutzavailable Pedersen)