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distributing entanglement in a multi-zone ion-trap

distributing entanglement in a multi-zone ion-trap. NIST, Boulder QC Group. 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. *.

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distributing entanglement in a multi-zone ion-trap

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  1. distributing entanglement in a multi-zone ion-trap NIST, Boulder QC Group 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 * at “entanglement and transfer of quantum information”: September 2004 * Division 891

  2. multiplexed trap architecture similar to Cirac/Zoller, but: one basic unit 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

  3. modularity reminder: 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

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

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

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

  7. Dk F universal two-qubit gate (e.g two qubits on stretch mode) k1 walking standing wave trap axis k2 coherent displacement beams Stretch mode excitation only for states Center-of-mass mode, wCOM = - F 2 F ¯ ­ Stretch mode, ws = D p k d 2 m w - w = w - d 2 1 stretch

  8. æ ö 1 0 0 0 ç ÷ eip/2 0 0 0 ç ÷ = G ç ÷ eip/2 0 0 0 ç ÷ ç ÷ 0 0 0 1 è ø universal geometric phase gate • Gate (round trip) time, tg = 2p/d • Phase (area), f = p/2 exp(i p/2) via detuningd via laser intensity exp(ip/2) Gives CNOT or p-phase gate with add. single bit operations

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

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

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

  12. General scheme: quantum dense coding A entangled state B one of four local operations on one qubit receiving two bits of information sending one qubit 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)

  13. quantum dense coding produce Alice’s entangled pair p/2-pulse and phase gate on both qubits rotate Alice’s qubit only sx, sy, szor no-rotation (identity) on Alice’s qubit, identity on Bob’s qubit Bob’s Bell measurement phase gate and p/2-pulse on both qubits Bob’s detection separate and read out qubits individually results: average fidelity 85%

  14. < measurement not only after an algorithm scalable QC needs error correction measurement as part of the algorithm Enhanced detection by QIP detection as bottleneck? coherent operations @ high fidelity state detection (read out) @ low fidelity output of an algorithm (e.g. Shor’s) yout = b0 |000…0> + b1 |000…1> + … + b2(N-1) |111…1> measurement projection in one of the 2N eigenstates with probability |bk|2 one qubit read out Fdet 1 state read out FNdet FNdet < 0.0008 e.g. Fdet= 0.70 and N = 20 FNdet = 0.82 e.g. Fdet = 0.99 and N = 20

  15. qubit (control) (a | + a | ) a |a1|a2 … |aM + QIP + a | |a1|a2 … |aM |a1|a2 … |aM e.g. CNOT’s M+1 tries error reduction > 40 % [only one ancilla (max. 99%)] ancillae (targets) results: D.P. DiVincenzo, S.C.Q. (2001) Enhance detection – how? statistical precision by repetition for Fdet < 1 FN shrinks exp. < (run algorithm many times) for Fdet ~ 1 still bad if tdet < talgorithm < statistical precision by reproduction (copy primary qubit many times) no cloning theorem statistical precision by amplification measure M+1 qubits (QIP on primary qubit and ancillae) (+ take majority vote)

  16. Dw/wo ~ 1/ N GHZ state (spectroscopy) Y = (| + eiw0t|) ·(| + eiw0t|)···(| + eiw0t|)/2N/2 projection noise limited: w0 non-entangled Heisenberg limited: Y = (|··· + exp(-iNt) |···)/21/2 Dw/wo ~ 1/ N entangled “superatom” Nw0 Entangled-states for spectroscopy (J. Bollinger et al. PRA, ’96) Experimental demonstration (two ions) (V. Meyer et al. PRL, ’01)

  17. GHZ state : results GHZ spectroscopy entanglement enhanced spectroscopy [gain by factor 1.45(2) over projection limit] GHZ state preparation P3 = … G3 = (p/2) (p) P3 (p/2):  YGHZ =   + i Total fidelity: F= áYGHZrYGHZ  = 0.89(3) (also in Innsbruck)

  18. Teleportation: Protocol Alice prepares state to be teleported ( a|­ñ2 + b|¯ñ2 )( |­ñ1|¯ñ3 - |¯ñ1|­ñ3 ) Alice performs Bell basis decoding on ions 1 and 2 Bob performs conditional rotation dep. on meas. Prepare ions in state |¯¯¯ñ and motional ground state Bob recovers a|­ñ + b|¯ñon ion 3 and checks the state Alice measures ion 1 Alice measures ion 2 Create entangled state on outer ions|­ñ1|¯ñ2|¯ñ3 - |¯ñ1|¯ñ2|­ñ3 (also in Innsbruck) Entire protocol requires ~2.5 msec

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

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

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

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

  24. Back to the Future:Boron-Doped Silicon 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… Joe Britton

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

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

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