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 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, 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 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 simulating solid state physics: 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 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 pick one: simulating quantum-spin-systems (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 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 computing versus adiabatic simulation -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 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 objective #1 investigate/exploit decoherence 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 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 objective #2 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