1. Quantum Information/Computing at DAMOP 2008 E. Gerjuoy

2. DAMOP 2008 QC/QI STATISTICS (I) Invited Paper sessions There were 28 invited paper sessions, containing 96 (typically half hour long) invited talks. Five of these sessions had titles which pretty explicitly indicated they would be of interest for quantum computing (qc) or quantum information (qi), e.g., “ Quantum Control of Polar Molecules, ” and “ Optical Quantum Memory. ” Three other sessions, though otherwise titled, contained one or more invited talks of qc/qi interest. All told, there were 17 invited papers whose abstracts indicated they would be of interest to qc/qi researchers. There were only 5 such invited papers at DAMOP 2007.

3. GRADUATE STUDENT THESIS SESSION Titles of Invited talks and Institutions where work was performed. 1.“Coherent Manipulation of Single Electronic and Nuclear Spins in Diamond.” Bates College and Harvard University. 2.“Towards Hybrid Quantum Information Processing With Polar Molecules.” University of Innsbruck, Austria and Austrian Academy of Science Institute for Quantum Optic and Quantum Information. 3.“Solid State Analogs in Bose-Condensed Gases.” MIT. 4.“Remote Entanglement and Quantum Networks with Trapped Ions.” University of Michigan.

4. ABSTRACT OF GURUDEV DUTT’S INVITED PAPER “Coupled Electronic and Nuclear Spin Quantum Registers in Diamond.” Building scalable quantum information systems is a central challenge facing modern science…We discuss experiments that demonstrate addressing, preparation, and coherent control of individual nuclear spin qubits in the diamond lattice at room temperature…Our results show that coherent operations are possible with individual solid-state qubits whose coherence properties approach those of isolated atoms and ions…[T]he nuclear spins serve as a resource for quantum memory and quantum logic operations.

5. Abstract of Invited Paper QC/QI “ Theory ” “ Toward Quantum Computing With Polar Molecules. ” David DeMille, Yale University The unique properties of polar molecules makes them potentially very attractive for quantum information processing. The rotational degree of freedom gives such molecules large polarizability at DC and microwave frequencies, enabling strong couplings between distant molecules … In this talk I will discuss evolving ideas for possible architectures to take advantage of these properties … I will also discuss our experimental progress towards this goal.

6. DAMOP 2008 QC/QI STATISTICS (II) Contributed Paper sessions There were 36 Contributed Paper sessions, with each session typically containing 10-12 ten minute talks. All told, there were a total of 27 ten minute papers on subjects of qc/qi relevance, with most of these papers in a pair of sessions titled: 1. “ Quantum Computation ” 2. “ Entanglement and Decoherence ” The counterpart numbers in DAMOP 2007 were a total of 47 ten minute talks on subjects of qc/qi relevance, with four Contributed Paper sessions largely devoted to qc/qi.

7. DAMOP 2008 QC/QI STATISTICS (III) There also were three Poster sessions, with a total of 431 posters. Two subsessions of these Poster sessions, titled respectively “ Quantum Information ” and “ Quantum Computation, ” contained a total of 10 posters. DAMOP 2007 did not have a “ Quantum Computation ” poster subsession, but its “ Quantum Information ” subsession contained 25 posters. As in DAMOP 2007, scattered through the various DAMOP 2008 Poster subsessions were other posters of qc/qi interest, e.g., a poster titled “ Experimental test of non-local realism …”

8. DAMOP 2008 Talks to be (Hopefully) Discussed 1.“ Remote Entanglement and Quantum Networks with Trapped Atomic Ions, ” DAVID MOEHRING, University of Michigan. Invited Paper, Graduate Student Thesis Session. 2.“ Geometric Phases and Bloch Sphere Constructions for SU(N), with a Complete Description of SU(4), ” DMITRY USKOV, Tulane University and RAVI RAU, Louisiana State University. Contributed 10 minute paper. 3. “ Quantum Computation Schemes Based On Polar Molecules, ” ELENA KUZNETSOVA et al, University of Connecticut and Harvard-Smithsonian Center for Astrophysics. Contributed 10 minute paper.

9. Abstract of David Moehring Talk “ The recent development of quantum information science and its potential applications have brought many of the fundamental questions of quantum physics to the mainstream … I discuss a system at the heart of these questions — quantum entanglement of the spin states of two individual massive particles at a distance … I present the theory and the experimental realization of the entanglement of two trapped atomic ions separated by one meter. Trapped ions are among the most attractive systems for scalable quantum information because they can be well isolated from the environment and manipulated easily with lasers. In particular, I discuss our results including the first explicit demonstration of both quantum entanglement between a single trapped ion and its single emitted photon, as well as entanglement between two macroscopically separated quantum memories. The entanglement protocols used in these experiments … can be used to create a platform for a scalable quantum information network or a distributed quantum computer …”

10. Outline of presentation Motivation –Why ion-trap quantum computing Background –Requirements for experiments with trapped ions –Requirements for remote entanglement of trapped ions Experimental results –Ion-photon and remote-ion entanglement –Bell inequality violations

11. Quantum Computing with Ions and Photons Ions: quantum memory –long-lived coherence (>10 seconds measured) –trapping times of days –near-perfect state initialization and detection Photons: quantum communication –coherence over long distances (kilometers)

12. Our Ion and Photon Qubits Ions: quantum memory –Hyperfine ground states ( 171 Yb + ) –Qubit rotations via microwaves or Raman beams Photons: quantum communication –Orthogonal polarizations/resolved frequencies –Qubit rotations with waveplates (polarizations) |V  |H  /2 || ||

13. 2 S 1/2 2 P 1/2 |  |  171 Yb + Ion-Photon Entanglement Polarization Qubits Matsukevich et al., PRL 100, 150404 (2008) Blinov, Moehring, Duan, Monroe, Nature 428, 153 (2004)

14. Ion-Photon Entanglement |H  |  - |V  |  Ion-Photon Entanglement Polarization Qubits 2 S 1/2 2 P 1/2 369 nm |  |  171 Yb + Photon Two different light polarizations |H  and |V  Ion Hyperfine ground states |  state is F=1, m=1 |  state is F=1, m=-1 |V|V |H|H Matsukevich et al., PRL 100, 150404 (2008) Blinov, Moehring, Duan, Monroe, Nature 428, 153 (2004) /4

15. Remote Ion Entanglement Polarization Qubits 2 S 1/2 2 P 1/2 369 nm |  |  171 Yb + Photon Two different light polarizations |H  and |V  Ion Hyperfine ground states |  state is F=1, m=1 |  state is F=1, m=-1 |V|V |H|H Ion-Photon Entanglement (|H  |  - |V  |  ) a  (|H  |  - |V  |  ) b Matsukevich et al., PRL 100, 150404 (2008)

16. Remote Ion Entanglement D BS D 2 distant ions Single Photon Detectors |  = (|H  a |  a - |V  a |  a )  (|H  b |  b - |V  b |  b ) |  i = |H  i |  i - |V  i |  i

17. Remote Ion Entanglement Polarization Qubits 2 S 1/2 2 P 1/2 369 nm |  |  171 Yb + Photon Two different light polarizations |H  and |V  Ion Hyperfine ground states |  state is F=1, m=1 |  state is F=1, m=-1 Coincidence projects ions onto: |  -  ions = |  a |  b - |  a |  b |V|V |H|H Ion-Photon Entanglement (|H  |  - |V  |  ) a  (|H  |  - |V  |  ) b Matsukevich et al., PRL 100, 150404

18. 2 S 1/2 2 P 1/2 369 nm |  |  171 Yb + Advantages Can decay directly to “clock qubit” Can allow for remote quantum gates directly Duan et al., PRA 73, 062324 (2006) Madsen, et al., PRL 97, 040505 (2006) Remote Ion Entanglement Frequency Qubits Disadvantages Difficult to characterize ion-photon entanglement

19. 2 S 1/2 2 P 1/2 369 nm 12.6 GHz |  |  171 Yb + Ion Hyperfine ground states |  state is F=1, m=0 |  state is F=0, m=0 Photon Two different light frequencies |R  and |B  Remote Ion Entanglement Frequency Qubits Moehring et al., Nature 449, 68 (2007)

20. 2 S 1/2 2 P 1/2 369 nm 12.6 GHz |  |  171 Yb + Ion Hyperfine ground states |  state is F=1, m=0 |  state is F=0, m=0 Photon Two different light frequencies |R  and |B  Ion-Photon Entanglement (|  |R  - |  |B  ) a  (|  |R  - |  |B  ) b Coincidence projects ions onto: |  -  ions = |  a |  b - |  a |  b Remote Ion Entanglement Frequency Qubits Moehring et al., Nature 449, 68 (2007)

21. Entangled!

22. Ion-Photon Bell Inequality Violation B(  A1,  A2 ;  B1,  B2 ) = q(  A2,  B2 )q(  A1,  B2 )q(  A2,  B1 )q(  A1,  B1 ) |q(  A2,  B2 ) - q(  A1,  B2 )| + |q(  A2,  B1 ) + q(  A1,  B1 )|  Matsukevich et al., PRL 100, 150404 (2008) Moehring et al., PRL 93, 090410 (2004)  photon  3  3   ion  q(  A1,  B2 ) -0.570.66-0.70-0.61 B( , 3  ; ,  ) = 2.54 (0.02) greater by 27  Yb + 369 nm

23. Remote Ion-Ion Bell Inequality Violation B(  A1,  A2 ;  B1,  B2 ) = q(  A2,  B2 )q(  A1,  B2 )q(  A2,  B1 )q(  A1,  B1 ) |q(  A2,  B2 ) - q(  A1,  B2 )| + |q(  A2,  B1 ) + q(  A1,  B1 )|  Matsukevich et al., PRL 100, 150404 (2008)  photon  3  3   ion  q(  A1,  B2 ) -0.580.57-0.52-0.55 B( , 3  ; ,  ) = 2.22 (0.07) greater by 3  Yb +

24. References D. N. Matsukevich, P. Maunz, D. L. Moehring, S. Olmschenk and C. Monroe Bell Inequality with Two Remote Atomic Qubits, Phys. Rev. Lett. 100, 150404 (2008). D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan and C. Monroe Entanglement of Single-Atom Quantum Bits at a Distance, Nature 449, 68-71 (2007). S. Olmschenk, K. C. Younge, D. L. Moehring, D. Matsukevich, P. Maunz, and C. Monroe Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit, Phys. Rev. A. 76, 052314 (2007). P. Maunz, D. L. Moehring, S. Olmschenk, K. C. Younge, D. N. Matsukevich and C. Monroe Quantum Interference of Photon Pairs from Two Remote Trapped Atomic Ions, Nature Physics 3, 538-541 (2007). D. L. Moehring, M. J. Madsen, K. C. Younge, R. N. Kohn, Jr., P. Maunz, L.-M. Duan, C. Monroe, and B. B. Blinov Quantum Networking with Photons and Trapped Atoms, J. Opt. Soc. Am. B, 24, 300-315 (2007). M. J. Madsen, D. L. Moehring, P. Maunz, R. N. Kohn, Jr., L.-M. Duan, and C. Monroe Ultrafast Coherent Coupling of Atomic Hyperfine and Photon Frequency Qubits, Phys. Rev. Lett. 97, 040505 (2006). L.-M. Duan, M. J. Madsen, D. L. Moehring, P. Maunz, R. N. Kohn, Jr., and C. Monroe Probabilistic Quantum Gates between Remote Atoms through Interference of Optical Frequency Qubits, Phys. Rev. A 73, 062324 (2006). D.L. Moehring, M. J. Madsen, B.B. Blinov, and C. Monroe Experimental Bell Inequality Violation with an Atom and a Photon, Phys. Rev. Lett. 93, 090410 (2004). L.-M. Duan, B. B. Blinov, D. L. Moehring, and C. Monroe Scalable Trapped Ion Quantum Computation with a Probabilistic Ion-Photon Mapping, Quant. Inf. Comp. 4, 165-173 (2004). B.B. Blinov, D.L. Moehring, L.-M. Duan, and C. Monroe Observation of entanglement between a single trapped atom and a single photon, Nature 428, 153-157 (2004). C6.09 K5.05

25. Abstract of Dmitry Uskov Talk Geometric Phases and Bloch Sphere Constructions for SU(N), with a Complete Description of SU(4). A two-sphere (“Bloch” or “Poincare”) is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2). We focus, in particular, on the SU(4) of two qubits which describe all possible logic gates in quantum computation. For a general Hamiltonian of SU(4) with 15 parameters we derive Bloch-like rotation of unit vectors analogous to the one familiar for a single spin in a magnetic field. See: Quant-ph 0801.2091.

26. 15 generators of the SU(4) group

27. We suggest an algebraic descriptions of dynamics of 2- dimentional subspaces of 4-leves systems in a form quite similar to the Bloch-vector description of 2-level density matrices, using transformed Plucker Coordinates on Grassmanian manifolds G(2,4,C) Six Plucker Coordinates are 6 minors of 2×4 matrix

28. To illustrate how the method may lead to some physical insights in a complicated non-stationary quantum problem consider two interacting qubits – the cornerstone problem in quantum information theory. The full dynamic group is 15-dimentional SU(4) group of unitary transformations. Present method allows to obtain semi-analytic solution for the Spin(5) 10-dimentional subgroup of the SU(4). The Hamiltonian of the problem has the form of a linear combination of ten generators with time-dependent coefficients. We group the latter in a form of 5×5 antisymmetric real matrix (for the purpose which will be clear shortly). Using common representation of su(4) generators as tensor products of standard Pauli matrices we write the Hamiltonian as

29. Abstract of Elena Kuznetsova Talk Polar molecules have recently attracted significant interest as a viable platform for quantum computing. They combine the advantages of neutral atoms and trapped ions, making them compatible with various architectures, e.g., optical lattices and solid-state systems. Molecules with large permanent dipole moments can display strong dipole-dipole interactions, allowing for the realization of fast conditional two-qubit gates. In recent work we proposed a model of controllable dipole-dipole interactions in which laser excitation from a ground electronic state with negligible dipole moment to an excited state with a large dipole moment allows one to “switch on” the interaction…We study the robustness of such a phase gate and analyze the experimental feasibility of the approach, using the CO molecule as a specific example. We are continuing to investigate several other schemes involving polar molecules and novel architectures such as a solid-state approach with polar molecules doped into rare-gas matrices. Kuznetsova, et al, Phys. Rev. A 78, 012313 (July 2008).

30. Why polar molecules? D. DeMille, Phys. Rev. Lett. 88, 067901 (2002) Rich level structure: electronic, vibrational, rotational states + electronic and nuclear spin statesRich level structure: electronic, vibrational, rotational states + electronic and nuclear spin states Long coherence timesLong coherence times Permanent electric dipole moment: strong dipole-dipole interactionsPermanent electric dipole moment: strong dipole-dipole interactions Manipulation with AC and DC electric fieldsManipulation with AC and DC electric fields Compatibility with various architectures, integration into solid-state systemsCompatibility with various architectures, integration into solid-state systems Scalability to large number of qubitsScalability to large number of qubits optical lattices superconducting stripline resonators + electrostatic traps Combine advantages of neutral atoms and trapped ions

31. Two-qubit phase gate with “switchable” dipoles |00› |00› → |00› → |00› → |00›, |01› → i|0e› → i|0e› → -|01›, i|e0› → |10› → i|e0› → i|e0› → -|10›, if φ=π |11› → -|ee› → - e iφ |ee› → |11› if φ=π π pulses |00›if φ=π |00› → |00› → e iφ |00› → - |00›, if φ=π |01› → i|0e› → i|0e› → -|01›, i|e0› → |10› → i|e0› → i|e0› → -|10›, |11› → -|ee› → - |ee› → |11› π pulses large dipole moment state zero dipole moment state direct scheme inverted scheme zero dipole moment state large dipole moment state

32. Molecular system for direct phase gate - 13 CO (carbon monoxide) Small μ state:Small μ state: ground X 1 Σ + state (μ=0.1 D) Large μ stateLarge μ state: metastable a 3 Π 0 state (μ=1.4 D) Qubit statesQubit states: nuclear spin states of 13 C (I=1/2) in X 1 Σ + state: state: entangled hyperfine sublevels of J=0 and J=1 of a 3 Π 0 state J=0J=0 X 1+X 1+ -1/2-1/2 +1/2 +1/2 F=1/2F=1/2 13CO13CO -3/2 J=0 F=1/2 -1/2 +1/2 J=1 a 3  0 F=1/2 F=3/2 +3/2 -1/2 +1/2 -1/2 +1/2 ~ 100 MHz 96 GHz -3/2 J=0 F=1/2 -1/2 +1/2 J=1 F=3/2 +3/2 -1/2 +1/2

33. Decoherence mechanisms Storage and switching states -Hyperfine states - lifetimes ~ hours -Metastable switching states - lifetimes ~ sec; phase gate times ~10-100 μ s - spontaneous emission is small phase gate times ~10-100 μ s - spontaneous emission is small -Dipole-dipole interaction – excitation of translational states of lattice potential – phase error; adiabatic excitation to large dipole moment states or use dipole blockade adiabatic excitation to large dipole moment states or use dipole blockade  Optical π and 2π pulses -Spatially varying Rabi frequency – imperfect pulse area load molecules to translational ground state load molecules to translational ground state  Optical lattice -Scattering of lattice photons - loss of molecules -Lifetimes in far-detuned lattices ~0.1 -1 s  Gate times ~ 100 μs, coherence times ~ 1 s – number of operations ~ 10 4 major decoherence source

34. Conclusions Polar molecules in an optical lattice represent an attractive platform for quantum computationPolar molecules in an optical lattice represent an attractive platform for quantum computation Polar molecules with “ switchable ” dipole moments allow one to realize a universal set of quantum gatesPolar molecules with “ switchable ” dipole moments allow one to realize a universal set of quantum gates Direct phase gate can be realized with molecules similar to CO, inverted scheme – with mixed alkali dimersDirect phase gate can be realized with molecules similar to CO, inverted scheme – with mixed alkali dimers Direct vs. inverted scheme:Direct vs. inverted scheme: Direct scheme can be electric-field free – more robust for decoherence Direct scheme can be electric-field free – more robust for decoherenceBut: cooling and trapping techniques are not available for general polar cooling and trapping techniques are not available for general polar molecules molecules Inverted scheme: Inverted scheme: ost polar molecules have large dipole moment in the ground state – most polar molecules have large dipole moment in the ground state – easier to find a candidate easier to find a candidate