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SP4 Quantum Simulation and Control

Quantum Simulation Quantum phase transitions (NMR, NV-Centres, Ion trap) Entanglement  Phase transitions General Hamiltonian simulation (NMR: 5 ... >10 qubits). Control of quantum evolution Use Optimal Control Theory to optimise quantum gates. explore decoherence free subspaces.

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SP4 Quantum Simulation and Control

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  1. Quantum Simulation Quantum phase transitions (NMR, NV-Centres, Ion trap) Entanglement  Phase transitions General Hamiltonian simulation (NMR: 5 ... >10 qubits) Control of quantum evolution Use Optimal Control Theory to optimise quantum gates. explore decoherence free subspaces. Apply to various experimental systems: Experimental demonstration of speed-up and robustness. Global control versus local control: Investigate efficiency, speed, quality, cost for entanglement generation and transfer of QI. Experimental probes for multi-particle entanglement. Develop new techniques to probe for systematic decoherence effects and their remedy. Effcient numerical simulation of spin networks. SP4 Quantum Simulation and Control 

  2. State dependent permanent electric dipole interaction enables ion-ion control ”Distillation” of qubits Quantum Simulation and ControlWP 4.1 Rare Earth Ion-Doped Crystals, S. Kröll, Lund Pr doped yttrium silicate crystal Hyperfine qubits Dipole interaction for cond. dynamics

  3. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Objectives within QAP (1st year) • Develop laser light source for coherent qubit operation. • Test single ion readout.

  4. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Achievements: • Laser source:coherence timeof 100 s (initially projected: 10 s). Free induction decay: Beat signal between laser and Pr ions (Pr:YSO)

  5. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Achievements: • Laser source:coherence timeof 100 s (initially projected: 10 s). Free induction decay: Beat signal between laser and Pr ions

  6. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Achievements: • Laser source: coherence timeof 100 s (initially projected: 10 s). Laser phase drift <5 over 10 ms Coherence time > 100 ms

  7. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Achievements: • Laser source: coherence timeof 100 s (initially projected: 10 s). Laser frequency drift  0.3 kHz/sec

  8. Quantum Simulation and ControlWP 4.1, Rare Earth Ion-Doped Crystals, S. Kröll, Lund Milestones 4.1.1 Agreement with TU Munich on what pulses to test for qubit operations • Delayed due to laser development 4.1.2 Fluorescence detection of qubits • Coherent readout technique preferred:excellent signal-to-noise, detection limit needs to be determined. Deliverables 4.1.1 Two-qubit operations tested with pulses derived using optimal control theory • Delayed due to laser development Status and Outlook Delays, however no show stoppers in sight. All exp. parts developed and tested perform as anticipated or better.Single ion readout: Scalable QC scheme (quant-ph/0601141). Single ion readout ion is under test.

  9. Generation of coupled defect center pairs: N2+ Ekin=7 keV ~5nm Diamond ~3nm Quantum Simulation and ControlWP 4.2, NV Defects in Diamond, J. Wrachtrup, Stuttgart Use single electron spin as read-out for nuclear/electron spin cluster; Use nuclear spins for simulations T. Gaebel et al., Nature Physics 2, 408 (2006)

  10. Quantum beats: Coherent coupling between two electron and a single nuclear spin. to 15N Quantum Simulation and ControlWP 4.2, NV Defects in Diamond, J. Wrachtrup, Stuttgart readout polarization Initialization and readout (optical) echo (t1=t2) Manipulation (microwaves) t2 t1 time T. Gaebel et al., Nature Physics 2, 408 (2006)

  11. Quantum Simulation and ControlWP 4.2, NV Defects in Diamond, J. Wrachtrup, Stuttgart • Coherent coupling to 4 different nuclei is demonstrated. • To come: coherent control in 3 spin system Hyperfine coupling to 13C and 15N 13C A B 15N L. Childress et al., Sciencexpress, Sept. 2006

  12. Quantum Simulation and ControlWP 4.2, NV Defects in Diamond, J. Wrachtrup, Stuttgart Milestones 4.2.1Generation of defect centre pairs with magnetic dipole interaction of 10 MHz and dephasing times larger than 0.1 ms. • Strong magnetic coupling > 10 MHz of NV-N . Phase memory 0.35 ms (Nature Physics 2, 408, 2006). 4.2.2 Observation of ground state spin coherence • Achieved. Deliverables 4.2.1Creation of defect centre pairs with distances less than 10 nm. • Pairs with  3 nm have been implanted 4.2.2Observation of ground state spin entanglement • Entanglement between two electron and a single nuclear spin. Status and Outlook Coherent coupling to 4 different nuclei demonstrated.Two and three-spin systems will be investigated: Determine phase memory. Entangle single electron spin with single nuclear spin.

  13. Quantum Simulation and ControlQuantum Compilation: a Control Problem

  14. Quantum Simulation and ControlWP 4.3, Optimal Control of Qu. Systems in Finite Dim. Milestones 4.3.1 Numerical simulation and optimal control of superconducting devices. • Capacitively coupled superconducting Josephson charge qubits: Q. optimal control provides shaped pulses that reduce the error rate of CNOT and TOFFOLI by two orders of magnitude with 5-fold speed-up (quant-ph/0504202). 4.3.2 Numerical simulation and optimal control of quantum gates in ion traps. • Single qubit gates implemented with trapped ions (see WP 4.6) Deliverables 4.3.1Computer programmes tailored to experimental techniques other than NMR • MATLAB interface to optimal-control based GRAPE algorithm can be adapted to experimental settings of QAP partners. Outlook Adapt optimisation tools to other experimental techniques Extend optimal control to cond. dynamics, e.g., with ion traps.

  15. Quantum Simulation and ControlWP 4.4, Modelling QC with 5 and more than 10 Qubits Milestones 4.4.1Numerical simulations on spin systems with 5 qubits. 4.4.2 Test on spin systems with 5 qubits and numerical simulations for 10 qubits. • Experimental tests up to 5 NMR spin qubits are successful. • Parallelised optimal-control-based GRAPE algorithm with speed-up >500 fold for 10 qubits on cluster of 128 CPUs compared to 1 CPU on same cluster (Proceedings EUROPAR 2006, LNCS 4128, 751, 2006). Deliverables 4.4.1Restricted test bed for quantum computational control on few-qubit systems. Extension of hardware beyond 10 qubits. • The synthetic work for NMR spin-system hardware beyond 10 qubits has faced unexpected chemical difficulties. Status and Outlook Future improvements beyond the goals of QAP will depend on progress in computer science.

  16. Quantum Simulation and ControlWP 4.5, Hamiltonian Simulation and DFS • Treated logical qubits embedded in a larger Liouville space of physical qubits by optimal control theory tailored to open dissipative systems. • Extended gradient-flow algorithm (GRAPE) to superoperators such as to find best approximations to a unitary target gate in the presence of dissipation (quant-ph/0609037). Milestones 4.5.1Establish limits on controllability in 2 and 3 qubits for ZZ, XY and XYZ coupling. • Controllability investigated up to systems of 4 physical qubits, e.g. in the KANE setting of nucleus-electron-electron-nucleus. 4.5.2 Establish limits on controllability in 3 qubits under Redfield-type relaxation. • Optimal control algorithms developed to give best approximations to unitary target modules in open systems.

  17. CNOT with dissipation optimal control: trace fidelity > 95% traditional methods, Trotter: < 15 % Quantum Simulation and ControlWP 4.5, Hamiltonian Simulation and DFS • Complete classification of locally reversible interaction Hamiltonians

  18. Spin-Spin coupling B Quantum Simulation and ControlWP 4.6Trapped Ion “Spin Molecule”, Chr. Wunderlich, Siegen Qubits: Hyperfine states Conditional quantum dynamics: Combine advantageous features of two “experimental wolrds”: NMR and Trapped Ions.

  19. Quantum Simulation and ControlWP 4.6Trapped Ion “Spin Molecule”, Chr. Wunderlich, Siegen Milestones 4.6.1 Ion Trap designed and built • Partially 4.6.2 Magnetic field generating elements designed and built. • Partially. Deliverables 4.6.1 A new ion trap with magnetic field elements ready. • Likely at the end of “true” month 12. Status and Outlook Progress roughly according to schedule Progress far ahead of schedule.

  20. Quantum Simulation and ControlWP 4.6Trapped Ion “Spin Molecule”, Chr. Wunderlich, Siegen Achievements • Isotope selective, nearly deterministic loading of ion trap.

  21. Probability Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. • Transfer of QI: Long distance: photons. Short distance: e.g., condensed matter systems. transfer speed, quality  spectral gap between ground and excited states  use as q. channel or as probe for spectral properties. M. Hartmann, M. Reuter and M.B. Plenio, New J. Phys. 8, 94 (2006)

  22. Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. Using only global control on a Ising-coupled spin chain: • Protocol for perfect transport of an unknown quantum state • Protocol for perfect quantum mirroring of the state of the chain about it’s middle. • Add local control to ends of chain: execute universal quantum computing on spins encoded onto the chain.J. Fitzsimons & J. Twamley, PRL 97, 090502 (2006) 1 qubit mirror Demonstrated in NMR J. Fitzsimons et al quant-ph/0606188 2 qubit gate

  23. Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. • Scaling laws for entanglement in general harmonic lattice system, andclassical correlations in a classical harmonic system. M. Cramer, J. Eisert, M.B. Plenio and J. Dreißig, Phys. Rev. A 73, 012309 (2006)

  24. Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. Energy gap between ground and first excited state decay of correlation functions in harmonic lattice systems on general graphs.  exponential decay of correlations for ground state and thermal states. M. Cramer and J. Eisert, New J. Phys. 8, 71 (2006)

  25. Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. Investigate dynamics of weakly driven chains of spin systems  quantum correlations in steady state when the noise strength exceeds threshold. Stochastic resonance. S. Huelga, M. Plenio,quant-ph/0608164

  26. Quantum Simulation and Control WP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. Entanglement transfer from two modes onto two atoms via local Jaynes-Cummings model Consider relation between entanglement, mixedness and energyMcHugh, Ziman, Buzek, PRA 74, 042303 (2006) Dependence on initial value of entanglement and initial energy of the photon field: entanglement between atoms initial entanglement initial energy

  27. Quantum Simulation and ControlWP 4.7 Entanglement Generation/Propagation, Phase Transitions V. Buzek, J. Eisert, S. Huelga, J.I. Latorre, M. Plenio Understand the static and dynamic entanglement properties of quantum many body systems. Deliverable 4.7.1. Simulation of a quantum algorithm on large quantum many body systems with up to 100 qubits. J.I Latorre

  28. Quantum Simulation and ControlWP 4.8 Protecting Quantum Memories • Laser cooling scheme for trapped ions based on the dynamical Stark shift gate.  Fast cooling to low final temperatures.A. Retzker and M.B. Plenio, quant-ph/0607199

  29. Quantum Simulation and ControlWP 4.9 Simulating q.phase transitions in ion traps, circuit QED, and optical lattices, V. Buzek, G. Milburn Milestones 4.9.1Specification of ion-trap models that can simulate quantum phase transitions. • Jahn-Teller like quantum phase transition with a single trapped ion, subject to a periodic impulsive force (Milburn et al., submitted). • Polaritons in array of cavities (photonic crystal or coupled micro-cavities): strongly interacting many body system, has potential as a quantum simulator (Imperial). 4.9.2 Specify experimental scheme for demonstrating a Jahn-Teller quantum phase transition in a circuit QED and ion trap. • Capacitive coupling of mechanical oscillator to a superconducting circuit (Milburn et al., submitted). Deliverables 4.4.1Develop ion trap schemes as analogue devices for obtaining information on the multipartite entanglement in the ground state of systems that undergo quantum phase transitions.

  30. Quantum Simulation and ControlWP 4.10 Q.State and Process Estimation, V. Buzek, S. Glaser, J.Twamley, J. Wrachtrup, • Problem: programmability of quantum devices in performance of quantum operations (CP maps), or quantum measurements (POVM). • Programs encoded in states of quantum system (program register) • Questions: universality, optimality, efficiency of deterministic, probabilistic and approximative devices. • Existence of universal programmable unambigous quantum state discriminator Bergou, Bužek, Feldman, Herzog, Hillery, Phys.Rev.A 73, 062334 (2006), Buzek, Hillery, Ziman, and Rosko, Quantum Information Processing 5, 313-420 (2006)

  31. Quantum Simulation and ControlWP 4.10 Q.State and Process Estimation, V. Buzek, S. Glaser, J.Twamley, J. Wrachtrup, Work shop on Q. Process Estimation:Budemerice, Slovakia, 28 Sept – 1. Oct. 2006

  32. Theory NV Centres n dn r n dn + + 1 1 1 2 2 r 2 Quantum Simulation and Control NMR Ion Trap Ion doped Crystal Theory

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