1. distributing entanglement in a multi-zone ion-trap * Division 891 T. Schätz D. Leibfried J. Chiaverini M. D. Barrett B. Blakestad J. Britton W. Itano J. Jost E. Knill C. Langer R. Ozeri T. Rosenband D. J. Wineland NIST, Boulder QC Group * at “entanglement and transfer of quantum information”: September 2004

2. multiplexed trap architecture interconnected multi-trap structure subtraps decoupled guiding ions by electrode voltages processor sympathetically cooled only three normal modes to cool no ground state cooling in memory no individual optical addressing during two-qubit gates gates in tight trap readout / error correction / part of single-qubit gates in subtrap no rescattering of fluorescence D. J. Wineland et al., J. Res. Nat. Inst. Stand. Technol. 103, 259 (1998); D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002). Other proposals: DeVoe, Phys. Rev. A 58, 910 (1998). Cirac & Zoller, Nature 404, 579 ( 2000). L.M. Duan et al., arXiv-ph\0401020 one basic unit similar to Cirac/Zoller, but:

3. modularity NIST array N  4N: ● no new motional modes ● no change in mode frequencies individually working modules will also work together “only” have to demonstrate basic module reminder:

4. 2 wafers of alumina (0.2 mm thick) gold conducting surfaces (2  m) 6 zones, dedicated loading zone 2 zones for loading 4 zones for QIP heating rate 1 quantum/6 ms (two-qubit gate in 10  s) Electrodes computer-controlled with DACs for motion and separation rf dc 200  m Filter electronics on board (SMD) (later: multiplexers, fibers, MEMS mirrors, detectors, sensors?) current trap design

5. universal set of gates universal two qubit gate (controlled phase gate): implemented with 97% fidelity. D. Leibfried et al., Nature 422, 414 (2003) single qubit rotations (around x,y or z-axis): experimentally demonstrated co-carrier rotations with > 99% fidelity. individual addressing despite tight confining 3m3m 30  m laser beam waist

6. individual addressing gate phase plot  /2 pulse effective individual Raman beams

7. universal two-qubit gate Stretch mode excitation only for states Center-of-mass mode, w COM Stretch mode, w s k1k1 k2k2 DkDk trap axis        stretch mdk FF 12 2 2 F walking standing wave coherent displacement beams (e.g two qubits on stretch mode)

8. universal geometric phase gate Gives CNOT or p-phase gate with add. single bit operations             1 0 00 0 00 0 00 0 0 01 G eip/2 eip/2 eip/2 eip/2 exp(i p / 2 )  Gate (round trip) time,  g = 2  /    Phase (area),  =  /2 via detuning d via laser intensity

9. experiments 1)distribution and manipulation of entanglement 2)quantum dense coding 3)QIP- enhancement of detection efficiency 4)GHZ-spectroscopy 5)teleportation 6)error correction “playing” with entanglement of massive particles two three qubits moving towards scalable quantum computation implement ingredients for multiplex architecture T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL (2004) T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL submitted (2004) D.Leibfried, M.D. Barrett, T.Schaetz et al., Science (2004) M.D. Barrett, J.Chiaverini, T.Schaetz et al., Nature (2004) J. Chiaverini, D.Leibfried, T.Schaetz et al., Nature submitted (2004)

10. DETECTOR individual addressing and entanglement distributed over two zones entangled pair distributed and manipulated entanglement survives distribution of entanglement DC-electrodes RF-electrode Fidelity: F=       = 0.85 No adverse effects from moving, individual rotation and separation

11. Distribution and manipulation of entanglement: results control triplet singlet Singlet (do individ. pulse after separation)    =  -  no rotation from final pulse, odd parity Triplet (no individ. pulse after separation)  +  =  +  rotates to  - e i   even parity Control (preparation only, no motion)  +  rotates to  - e i   even parity no adverse effects from moving, individual rotation and separation Fidelity: F=       = 0.85

12. quantum dense coding one of four local operations on one qubit receiving two bits of information sending one qubit entangled state General scheme: Theoretically proposed by Bennett and Wiesner (PRL 69, 2881 (1992)) Experimentally realized for ‘trits’ with photons by Mattle, Weinfurter, Kwiat and Zeilinger (PRL 76, 4656 (1996)) only two Bell states identifiable, other two are indistinguishable ( trit instead of bit) non deterministic (30 photon pairs for one trit) (but: photons light and fast) A B

13. I xx yy zz  0.840.070.060.03  0.020.030.080.87  0.070.010.840.08  0.080.840.04 average fidelity 85% quantum dense coding produce Alice’s entangled pair  / 2-pulse and phase gate on both qubits rotate Alice’s qubit only  x,  y,  z or no-rotation (identity) on Alice’s qubit, identity on Bob’s qubit Bob’s Bell measurement phase gate and  /2-pulse on both qubits Bob’s detection separate and read out qubits individually results:

14. Enhanced detection by QIP coherent operations @ high fidelity state detection (read out) @ low fidelity detection as bottleneck? y out = b 0 |000…0> + b 1 |000…1> + … + b 2 (N-1) |111…1> measurement projection in one of the 2 N eigenstates with probability | b k | 2 one qubit read out F det 1 state read out F N det < e.g. F det = 0.70 and N = 20 F N det < 0.0008 e.g. F det = 0.99 and N = 20 output of an algorithm (e.g. Shor’s) F N det = 0.82 measurement not only after an algorithm scalable QC needs error correction measurement as part of the algorithm

15. Enhance detection – how? statistical precision by repetition (run algorithm many times) statistical precision by reproduction (copy primary qubit many times) statistical precision by amplification (QIP on primary qubit and ancillae) measure M+1 qubits (+ take majority vote) for F det < 1 F N shrinks exp.< for F det ~ 1 still bad if t det < t algorithm < no cloning theorem (a |  + a |  ) qubit (control) ancillae (targets ) a  |  a1 |  a2 … |  aM + |  a1 |  a2 … |  aM + a |  |  a1 |  a2 … |  aM M+1 tries QIP e.g. CNOT’s D.P. DiVincenzo, S.C.Q. (2001) error reduction > 40 % [only one ancilla (max. 99%)] results:

16. 00  = ( |  + e i  0 t |  ) ·( |  + e i  0 t |  )···( |  + e i  0 t |  )/2 N/2  = ( |  ···  + exp(-iN  t) |  ···  )/2 1/2  0 entangled “superatom” Entangled-states for spectroscopy (J. Bollinger et al. PRA, ’96) non-entangled Experimental demonstration (two ions) (V. Meyer et al. PRL, ’01) GHZ state (spectroscopy) projection noise limited: Heisenberg limited: Dw/w o ~ 1/ N

17. GHZ state : results -i0000000 01000000 00100000 000 0000 00001000 00000 00 000000 0 00000001 P 3 = … GHZ state preparation entanglement enhanced spectroscopy [gain by factor 1.45(2) over projection limit] GHZ spectroscopy G 3 = (  /2) (  ) P 3 (  /2):       GHZ  =    + i    Total fidelity: F=   GHZ     GHZ  = 0.89(3) -i0000000 01000000 00100000 000 0000 00001000 00000 00 000000 0 00000001 (also in Innsbruck)

18. Prepare ions in state  and motional ground state Create entangled state on outer ions             Alice prepares state to be teleported              Alice performs Bell basis decoding on ions 1 and 2 Alice measures ion 1Alice measures ion 2 Bob performs conditional rotation dep. on meas. Bob recovers      on ion 3 and checks the state Entire protocol requires ~2.5 msec (also in Innsbruck) Teleportation: Protocol

19. Error correction basics Encode a logical qubit state into a larger number of physical qubits (here 1 logical qubit in (3 – large?) physical qubits) Make sure that your logical operations leave the state in one part of the total Hilbert space while your most common errors leave that part Construct measurements that allow to distinguish the type of error that happened Do those measurements and correct the logical state according to their outcome classical strategy: redundancy by repetition (0  00…0, 1  11…1 and majority) quantum analog: repetition code (see e.g. Nielsen and Chuang)

20. ● experimental error correction with classical feedback from measured ancillas ● no classical analog 3 qubit bitflip error-correction encoding/decoding gate (G) implemented with single step geometric phase gate example data (error angle) 2 Infidelity (1-F) J. Chiaverini et al., submitted

21. Experiments “playing” with entanglement of massive particles moving towards scalable quantum computation 1)separation and transfer of qubits between traps 2)maintaining entanglement 3)individual addressing (in tight confinement) 4)single and two qubit gates 5)use of DFS (Decoherence Free Subspace) 6)use of ancilla qubits (trigger conditional operations) 7)pushing QIP fidelities principally towards fault tolerance 8)non-local operations / teleportation (including “warm gate”) 9)step towards fault tolerance ( 3 qubit error correction) 10)(sympathetic cooling)

22. It is not over, just a start… (fault tolerance) reduce main sources of error (e. g. beam intensity), demonstrate error correction and make it routine tool test new traps using reliable ways of “mass fabrication”, (lithography, etching, etc.) incorporate microfabricated electronics and optics (multiplexers, DACs, MEMS mirrors ect.) IV. “scale” electronics and optics to be able to operate in larger arrays III. build larger trap arrays II. reach operation fidelity of > 99.99%, incorporate error correction I. incorporate all building blocks with sympathetic cooling in one setup more complicated algorithms

23. New Trap Technology Approaches to the necessary scale-up for trap arrays…

24. almost arbitrary geometries very small precise features atomically smooth mono-crystaline surfaces incorporate active and passive electronics right on board filters, multiplexers, switches, detectors incorporate optics MEMS mirrors, fiberports… Back to the Future: Boron-Doped Silicon Joe Britton

25. Future techniques II  Control electrodes on outside easy to connect “X” junctions more straightforward Field lines: dc rf dc rf dc Pseudopotential: Planar 5 wire trap John Chiaverini

26. Planar Trap Chip DC Contact pads RF Gold on fused silica John Chiaverini low pass filters trapping region