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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 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 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 readout / error correction / part of single-qubit gates in subtrap no rescattering of fluorescence modularity NIST array N4N: ● no new motional modes ● no change in mode frequencies individually working modules will also work together “only” have to demonstrate basic module reminder: current trap design 2 wafers of alumina (0.2 mm thick) gold conducting surfaces (2 mm) dc rf rf dc 6 zones, dedicated zone Filter electronics onloading board (SMD) 200 mm 2 zones for loading fibers , (later: multiplexers, 4MEMS zones mirrors, for QIP detectors, sensors?) heating rate 1 quantum/6 ms (two-qubit gate in 10 ms) Electrodes computer-controlled with DACs for motion and separation universal set of gates single qubit rotations (around x,y or z-axis): experimentally demonstrated co-carrier rotations with > 99% fidelity. individual addressing despite tight confining 30mm laser beam waist 3mm universal two qubit gate (controlled phase gate): implemented with 97% fidelity. D. Leibfried et al., Nature 422, 414 (2003) individual addressing gate phase plot Raman beams effective individual p/2 pulse universal two-qubit gate (e.g two qubits on stretch mode) w2 k1 d Dk w1 k2 trap axis walking standing wave F coherent displacement beams F = -2 F D k d = 2 pm w 2 - w1 = w stretch - d Stretch mode Center-of-mass mode, wCOM excitation Stretch mode, ws only for states , universal geometric phase gate Gate (round trip) time, tg = 2p/d via detuning d exp(i p/2) Phase (area), f= p/2 via laser intensity 1 0 0 p 0 ei /2 0 G= ip/2 e 0 0 0 0 0 1 0 0 0 Gives CNOT or p-phase gate with add. single bit operations exp(i p/2) experiments 1) distribution and manipulation of entanglement 2) quantum dense coding T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL (2004) two “playing” with entanglement of massive particles qubits 3) QIP- enhancement of detection efficiency T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL submitted (2004) 4) GHZ-spectroscopy 5) teleportation M.D. Barrett, J.Chiaverini, T.Schaetz et al., Nature (2004) three D.Leibfried, M.D. Barrett, T.Schaetz et al., Science (2004) 6) error correction J. Chiaverini, D.Leibfried, T.Schaetz et al., Nature submitted (2004) moving towards scalable quantum computation implement ingredients for multiplex architecture distribution of entanglement DETECTOR Fidelity: F=DC-electrodes YrY = 0.85 or i - singlet does not iodd triplet singlet rotate parity entangled individual addressing pair distributed and and manipulated entanglement survives distributed over two zones ( I) 22 ( 2 ) p p ppp p p p Phase Gate (f ) (f ) 2 2 222 No adverse effects from moving, RF-electrode individual rotation and separation 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) Fidelity: F= YrY = 0.85 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 control triplet singlet quantum dense coding General scheme: A entangled state B one of four local operations on one qubit 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) receiving two bits of information quantum dense coding produce Alice’s entangled pair p/2-pulse and phase gate on both qubits rotate Alice’s qubit only sx, sy, sz or 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: I sx sy sz 0.84 0.07 0.06 0.03 0.02 0.03 0.08 0.87 0.07 0.01 0.84 0.08 0.08 0.84 0.04 0.04 average fidelity 85% Enhanced detection by QIP coherent operations @ high fidelity state detection (read out) @ low fidelity detection as bottleneck? 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 e.g. Fdet = 0.70 and N = 20 e.g. Fdet = 0.99 and N = 20 state read out FNdet FNdet < 0.0008 FNdet = 0.82 measurement not only after an algorithm scalable QC needs error correction measurement as part of the algorithm Enhance detection – how? statistical precision by repetition (run algorithm many times) for Fdet<< 1 FN shrinks exp. statistical precision by reproduction (copy primary qubit many times) statistical precision by amplification (QIP on primary qubit and ancillae) for Fdet ~ 1 still bad if tdet << talgorithm no cloning theorem measure M+1 qubits (+ take majority vote) qubit (control) (a| + a | ) |a1|a2 … |aM QIP e.g. CNOT’s a a |a1|a2 … |aM + | |a1|a2 … |aM M+1 tries ancillae (targets) D.P. DiVincenzo, S.C.Q. (2001) results: error reduction > 40 % [only one ancilla (max. 99%)] GHZ state (spectroscopy) Y= (| + eiw t|) ·(| + eiw t|)···(| + eiw t|)/2N/2 0 0 0 projection noise limited: w0 Dw/wo ~ 1/ N non-entangled Y= (|··· + exp(-iNwt) |···)/21/2 Heisenberg limited: Nw0 entangled “superatom” Dw/wo ~ 1/ N Entangled-states for spectroscopy (J. Bollinger et al. PRA, ’96) Experimental demonstration (two ions) (V. Meyer et al. PRL, ’01) GHZ state : results GHZ state preparation P3 = … G3 = (p/2) -i 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -i 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -i 0 0 0 0 0 0 0 0 -i 0 0 0 0 0 0 0 0 1 (p) P3 (p/2): YGHZ = + i Total fidelity: F= YGHZrYGHZ = 0.89(3) (also in Innsbruck) GHZ spectroscopy entanglement enhanced spectroscopy [gain by factor 1.45(2) over projection limit] Teleportation: Protocol Alice state to be Alice performs Bobprepares performs Prepare ions in conditional state Bob Alice Alice recovers measures measures a b ion ion 12on teleported Create entangled state on outer Bell decoding rotation dep. onbasis meas. and motional ground state 3 and checks (a 13 -1the 32) ionsion 3 1state 2b 2 )( 1 on 12 3 - ions 2and Entire protocol requires ~2.5 msec (also in Innsbruck) 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, 111…1 and majority) quantum analog: repetition code (see e.g. Nielsen and Chuang) a b a b 3 qubit bitflip error-correction Infidelity (1-F) ● experimental error correction with classical feedback from measured ancillas ● no classical analog (error angle)2 encoding/decoding gate (G) implemented with single step geometric phase gate example data J. Chiaverini et al., submitted Experiments “playing” with entanglement of massive particles moving towards scalable quantum computation 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 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) 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.) New Trap Technology Approaches to the necessary scale-up for trap arrays… 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 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 Planar Trap Chip Gold on fused silica RF DC Contact pads John Chiaverini trapping region low pass filters