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QAP – SP4 Quantum Simulation & Control

QAP – SP4 Quantum Simulation & Control. Quantum Simulation and Control. Experiment: Develop and advance spin systems suitable for quantum simulations creation and analysis of entanglement robust and optimised quantum gates characterize and control decoherence.

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QAP – SP4 Quantum Simulation & Control

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  1. QAP – SP4 Quantum Simulation & Control

  2. Quantum Simulation and Control Experiment: Develop and advance spin systems suitable for quantum simulations creation and analysis of entanglement robust and optimised quantum gates characterize and control decoherence Develop technology and protocols for • few-qubit quantum information processing • quantum simulation • Theory: • analyze static and dynamic properties of quantum many body systems • simulate 1-D quantum systems with >50 qubits. • Optimal control theory

  3. Quantum Simulation and ControlWP4.1 Objective and Approach • Objective • Several qubit QC based on rare-earth-ion doped crystalsTestbed for optimum pulses and pulse sequences. • Approach • Ensemble implementation; a few qubits. • Individual qubits based on single ion readout; more qubits. Pr doped yttrium silicate crystal

  4. Quantum Simulation and Control laser 2 1 readout q1 q2 q3 |e q1  q4 q5 readout ion q6 2 + 1 1 fluorescence q7 laser 1 2 |1 |0 dipole-dipole interaction lWP4.1 Selected results The readout ion concept for the single instance many-qubit implementation. The qubit |0>-|e> transition turns off the fluorescence

  5. Quantum Simulation and Control lWP4.1 Selected results Achievements: Ce3+ as readout ion for single instance many-qubit implementations Ce3+ 4f-5d transition in Y2SiO5 : • identified near 370.6 nm • inhomogeneous line width: 80 GHz • homogeneous line width: 3 MHz (limited by upper state lifetime of 50 ns)Importantly, homogeneous line width is narrower than expected!!! qubit-readout ion distance up to several nm possible (D4.1.3 and M4.1.3). • Simulations (M4.1.4) show that interacting several qubit structures will be present in Y2SiO5 at Pr concentrations of the order of 1% • Experiments to detect single Ce3+ ions are now starting

  6. Quantum Simulation and Control 0.6 0.4 Absorption, αL 0.2 Two-level transfer efficiency vs. pulse bandwidth 0 100 -2 0 2 4 6 8 10 12 14 16 Frequency (MHz) 80 60 Pulse fidelity (%) 40 "Optimal" Rabi frequency 20 Max available Rabi frequency 0 1 10 Bandwidth (MHz) 0.6 0.4 Absorption, αL 0.2 0 -2 0 2 4 6 8 10 12 14 16 Frequency (MHz) lWP4.1 Deliverables D4.1.4: Test of pulse sequences for two-qubit entanglement Initialized to the |0> state Searching for better pulse shapes with optimal control techniques 1/2 – hyperfine state (8 ms) (4 ms) (2 ms) (2 ms) Optimal control pulse with 8 MHz bandwidth Transfer to |1> state 3/2 – hyperfine state |exc> |0> |1>

  7. Quantum Simulation and Control lWP4.1 Deliverables D4.1.4: Test of pulse sequences for two-qubit entanglement Single-qubit operations (>0.9 fidelity) with quantum state tomography* now in an undergraduate lab!! Qubit-qubit interaction previously demonstrated. However, need faster operations for qubit entanglement. Shorter duration single-qubit operation pulse sequences developed by TU Munich are presently tested. In order to fulfil the deliverable in time: attempt two-bit entanglement with pulses (TU Munich) that already were implemented successfully. *“Experimental quantum state tomography of a solid state qubit”, L Rippe, B Julsgaard, A Walther, Yan Ying, S Kröll, Phys Rev A77, 022307 (2008). http://lanl.arxiv.org/abs/0708.0764,

  8. Quantum Simulation and Control lWP4.2 Selected Results Goal: Use nuclear spins around NV to simulate properties of multispin cluster with adjustable interaction. Free induction decay of NV defect in ultrapure diamond. This decay is the longest FID for any solid state system.

  9. Quantum Simulation and Control . E 0 p p p coherence transfer D 4.2.4 Entanglement of three qubits in diamond.  x  y nut. N1 0.39 p Generation of GHZ and W states from 1 electron spin and 2 nuclear spins (13C) N2 p/2 t Detection Preparation Entanglement W-state= τ = 0 τ = 4.4 µs Neumann et al., Science 320, 1326 (2008)

  10. Quantum Simulation and Control lWP4.3 Optimal Control of Quantum Systems: Selected Results D4.3.3 Extension of MATLAB package to … broader array of experimental settings   [TEG1-06], [DHK1-07],[SDH1-07]. NEW: optimal control for generating cluster states in ion spin molecule

  11. Quantum Simulation and ControlWP4.4 and WP4.5 Selected Results Scalable Quantum CISC Compiler by Optimal Control exploiting 128 parallel nodes on cluster HLRB-II (9728 n: total LINPACK performance of 63.3 TFlops/s) CISC-Compiler fast, decoh.-protected principle: use m-qubit interaction building blocks to fight decoherence • m=2: standard universal gate decomposition, RISC (restricted instruction set: CNOT) • m>2: enlarge toolbox to recursively usable m-qubit complex instruction sets (CISC) Schulte-Herbrüggen, Spörl, Glaser: quant-ph/0712.3227

  12. Quantum Simulation and ControlWP4.4 and WP4.5 Selected Results Scalable Quantum CISC Compiler for Large-Scale Q-Computing Example: C NOT (generalised TOFFOLI, multiple-controlled NOT on Ising spin chain) vast improvement by assemblingm-qubit CISCmodules against 2-qubit RISC standard n time costquality improvement RISC estim. limit CISC CISC CISC estim. limit RISC Schulte-Herbrüggen, Spörl, Glaser: quant-ph/0712.3227

  13. Quantum Simulation and ControlWP4.4 and WP4.5 Selected Results By-Product: Faster General Construction for Multiply-Controlled Unitary Gates n time costnew general C U construction: RISC faster than the classical scheme in Barenco et al., PRA 52 (1995) 3457 CISC new estim. limit Schulte-Herbrüggen, Spörl, Glaser: quant-ph/0712.3227

  14. Quantum Simulation and ControlWP4.6 Ion Trap Quantum Simulation using Ion Spin Molecule Yb+ Single N-spin “designer molecule”: • Adjustable coupling constants Jij . • Individual addressing of spins. • Insensitive to thermal motion Quantum Simulations: Phase Transitions. Entanglement and Decoherence. Neural Network (M. Pons et al., Phys. Rev. Lett. 98, 023003, 2007)

  15. Quantum Simulation and ControlWP4.6 Selected Results Ion Spin Molecule: Spin-Motion Coupling using rf radiation

  16. Quantum Simulation and ControlWP4.6 B New Trap Set-up for Ion Spin Molecules: M 4.6.3 Laser light sources (369 nm, 935 nm and 638 nm) are ready. Optical components for imaging of in the uv range have been developed and built. M 4.6.4 New vacuum recipient with all optical and electrical interfaces is built, leak tested and ready to mount ion trap. M 4.6.5 Implement individual addressing in frequency space x

  17. Quantum Simulation and ControlWP4.7 Selected Results M4.7.5 Quantum circuit for 4-qubit Quantum Ising model Verstraete, Cirac, Latorre, arXiv.org:0804.1888 U Prepare a product state Obtain the Ising ground state

  18. Quantum Simulation and ControlWP4.7 Selected Results M4.7.6 Entanglement scaling for Matrix Product States Tagliacozzo, de Oliveira, Iblisdir, Latorre, Phys. Rev. B 78, 024410 (2008) Emergence of χ-scaling: Displacement of fixed point Magnetization Half-chain entropy Correlation length

  19. Quantum Simulation and ControlWP4.7 Selected Results Density-matrix renormalization group (DMRG) in the Heisenberg picture (H-DMRG): • Efficiency of approximation much better, as only the observable of interest but not the entire state is considered. • In some non-trivial cases, H-DMRG can be exact for finite bond dimensions. Hartmann & Plenio, E-print arXiv:0808.0666 [quant-ph]

  20. Quantum Simulation and ControlWP4.8 Selected Results M 4.8.5 Propose scheme for the experimental observation of quantum phase transition in ion traps.  Retzker, Thompson, Segal, Plenio, arXiv:0801.0623

  21. Quantum Simulation and ControlWP4.8 Selected Results Hopping Hamiltonian Dissipation Dephasing Plenio & Huelga, arXiv:0807.4902

  22. Quantum Simulation and ControlWP4.8 Selected Results Plenio & Huelga, arXiv:0807.4902 Coherent coupling strength in Fenner-Matthews-Olson chromophore complex local site loss rate No decoherence: probability that excitation in site 1 reaches sink Optimized decoherence rates probability that excitation in site 1 reaches sink Simple demonstration proposed in ion trap set-up

  23. Quantum Simulation and ControlWP4.8 Selected Results Unruh Effect: a Uniform acceleration • Need a quantum field with a low “speed of light” • Need a detector that is sensitive to very low temperatures • Yields more moderate acceleration requirement

  24. BEC AQD Quantum Simulation and ControlWP4.8 Selected Results Cigar shaped BEC Narrow optical dipole trap Retzker, Cirac, Plenio, Reznik, Phys. Rev. Lett. 101, 110402 (2008)

  25. Quantum Simulation and ControlWP4.8 Selected Results lSimulate local relaxation phenomena in quantum many-body systems: lConsider sudden “quenches” from one nearest-neighbor Hamiltonian to another l“Dynamics of quantum phase transitions”, “apparent relaxation phenomena” lQuantum simulations with cold atoms in optical superlattices Cramer, Dawson, Eisert, Osborne, Phys Rev Lett 100 (2008) Cramer, Flesch, McCulloch, Schollwoeck, Eisert, Phys Rev Lett101 (2008)

  26. Quantum Simulation and ControlWP4.8 Selected Results M.J. Hartmann, F.G.S.L. Brandão and M.B. Plenio“Complex dynamics in coupled arrays of micro-cavities”Invited review for Laser & Photonics Review 2008 and E-print arXiv:0808.2557 [quant-ph]

  27. Quantum Simulation and ControlWP4.8 Selected Results Jahn-Teller model in ultra strongly coupled circuit QED. a,a†: cavity field |n>, number of Cooper pairs on junction

  28. Quantum Simulation and ControlWP4.8 Selected Results Derived Hamiltonian: Coupling scales as inverse root of fine structure constant Much stronger than cavity QED Cannot make the rotating wave approx.

  29. … c,c† … b,b† … a,a† WP4.9: Generation and protection of multi-qudit entangled states for cluster states and investigation of phase transitions-Selected Results Multimode bosonic system with a total of n bosons distributed between modes. Prepare modes in Fock states  entangled state (occup. number) Interaction with phase sensitive reservoir (‘squeezed vacuum’)  steady state is multimode entangled. Resource for cluster state generation, quantum phase transitions For example, a steady state of a 4-mode system with two bosons is

  30. WP4.9: Generation and protection of multi-qudit entangled states for cluster states and investigation of phase transitions-Selected Results Decay Rate of Cyclotron Modes Each mode is represented by one trapped electron, Two trapped electrons are enclosed in a cavity resonant with a transition frequency ω, Axial frequency of a trapping potential is ωz, Electric field on the electrode frequency is ωc, Distance between two traps/electrons is d,

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