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Quantum Information Science Q with Trapped Ions

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Quantum Information Science Q with Trapped Ions Quantum Information Science with Trapped Ions 4 Quantum Information Science EitlExperimental IlImplement ttiation with TdTrapped Ions Rainer Blatt Institute of Exppy,y,erimental Physics, University of Innsbruck, Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences Lectures: 3. Advance d procedures and operations teleportation, entanglement swapping etc. 4. Scaling up the ion trap quantum processor segmented traps; complex, fast procedures 3. Quantum information processing with trapped Ca+ ions 2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 222.2 Cirac-Zo ller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 3.2 Entanglement Swapping 3.3 Metrology with entangled states 4.0 Scaling the ion trap quantum computer Teleportation recover input state measurement in Bell basis ALICE unknown input state rotation Bell state BOB M. Riebe et al., Nature 429, 734 (2004) M.D. Barrett et al., Nature 429, 737 (2004) Teleportation M. Riebe et al., Alice‘s input state New J. Phys. 9, 211(2007) Alice and Bob share the state joint three-qubit quantum state can be written as rearrange with Quantum teleportation protocol classical communication Ion 1 Ion 2 C Bell Ion 3 state CNOT operation, conditional check BllbBell bas is #2 and #3 rotations on #3 #3 entangled Bell recovered initialize state measurement on #3 #1, #2, #3 prepared on #1 QCSL: Quantum Computer Script Language Quantum teleportation protocol, details conditional rotations Ion 1 using electronic logic, B B B B C C H triggered by PM signal Ion 2 C B B B C H U H Ion 3 C H U C H U C C C C spin echo sequence blue sideband B pulses full sequence: carrier pulses 26 pulses + 2 measurements C Teleportation procedure, analysis Initial Input state Output state Final U TP U-1 Fidelities Teleportation with atoms: results 83 % class. : 67 % no cond. op. 50 % - no post-selection - teleportation at "any" choice of time - it wor ks "a lways " M. Riebe et al., New J. Phys. 9, 211(2007) - only 10 m Process tomography of quantum teleportation M. Riebe et al., New J. Phys. 9, 211(2007) Process tomography of quantum teleportation represent input/output states with Bloch spheres: inppput sphere output sphere M. Riebe et al., New J. Phys. 9, 211(2007) 3. Quantum information processing with trapped Ca+ ions 2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 222.2 Cirac-Zo ller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 3.2 Entanglement Swapping 3.3 Metrology with entangled states 4.0 Scaling the ion trap quantum computer Entanglement swapping: entanglement transfer protocol ► entanglement swapping : distribution of entanglement two atoms that never interacted become entangled atom – light entanglement by postselection: expect: /2 Bell yy pair ograph Bell mm pair To measurement of qubits 2 and 3 finds either and leave qubits 1 and 4 in one of the Bell states Entanglement swapping: action upon measurement conditional rotations of qqpgubit 3 depending on outcome of measurement of qubits 1 and 4 deterministic entanglement of qubits 2 and 3 Bell /2 pair raphy gg Z X Bell pair Tomo M. Riebe et al., Nature Physics 4, 839 (2008) Pulse sequence for entanglement swapping Bell12 CNOT C B B B C C’ C’ B C’ C C’ C C’ B C’ C C’ C C’ C C C C B C B B B C C’ C’ hide states spin Bell 34 (protect) echoes Entanglement swapping: result tomography analysis of final state: still violates Bell inequality: M. Riebe et al., Nature Physics 4, 839 (2008) 3. Quantum information processing with trapped Ca+ ions 2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 222.2 Cirac-Zo ller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 3.2 Entanglement Swapping 3.3 Metrology with entangled states 4.0 Scaling the ion trap quantum computer Quantum metrology with trapped ions ….using entanglement for precision measurements Detection enhancement using entangling operations T. Schätz et al., Phys. Rev. Lett. 94, 010501 (2005) Enhancing the S/N ratio using more entangled atoms/ions D. Leibfried et al., Science 304, 1476 (2004), Nature 438, 639 (2005) Entangling spectroscopy ions with logic ions using quantum information processing P. Schmidt et al., Science 309, 749 (2005) Designing entangled atoms for precision measurements C. F. Roos et al., Nature 443, 316 (2006) Ion clocks with entangled states Clock experiments with maximally entangled states (Wine lan d e t a l., PRA 46, R6797(‘92), Bo llinger e t a l., PRA 54, R4649 (‘96)) /2 pulses + parity measurement measurement uncertainty 3. Quantum information processing with trapped Ca+ ions 2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 2.2 Cirac-Zoller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 323.2 Entanglement Swapping 3.3 Metrology with entangled states 404.0 Scaling the ion trap quantum computer 4.1 More complex and faster procedures Scaling the ion trap quantum computer …. more ions, larger traps, phonons carry quantum information Cirac-Zoller, slow for many ions (few 10 ions maybe possible) move ions, carry quantum information around Kielpinski et al., Nature 417, 709 (2002) requires small, integrated trap structures, miniaturized optics and electronics Multiplexed trap structure: NIST Boulder D. Leibfried, D. Wineland et al., NIST Operating a quantum algorithm on an ion chip Movie: © Isaac Chuang, MIT Operating a quantum algorithm on an ion chip Movie: © Isaac Chuang, MIT The development of a quantum microprocessor Innsbruck ion trap since 2000 ion trap chip 2008, microtrap Scaling the ion-trap quantum computer: CHIPS Planar chip traps: Wineland group (J. Chiaverini, S. Seidelin) Lucent: DSlhD. Slusher e t a l. Ion Chip Trap Quantum Microprocessors: worldwide efforts d ~ 40µm d ~ 250µm MIT, USA NIST, USA Ulm + Microtrap d ~ 200µm d ~ 200µm U Michigan, U Maryland, USA USA d ~ 60µm U Innsbruck Advanced chip traps at NIST 2-layer, 2-D, X-junction, 18 zones (Au on Al2O3) Transport through junction (9Be+,24Mg+) minimal heating ~ 20 quanta transport error < 3 x 10-6 R. B. Blakestad transport in 40-zone, surface-electrode trap (Au on quartz) multi-layer leadouts louvers for back-side loading 4 mm (prevents electrode shorting) J. Amini Next (?) 200 – zone “racetrack” Scaling the ion trap quantum computer: CHIPS Monroe group Scaling the ion trap quantum computer …. cavity QED: atom – photon interface, use photons for networking J. I. Cirac et al., PRL 78, 3221 (1997) P. Schmidt et al., Univ. Innsbruck trap arrays, using single ion as moving head motion head I. Cirac und P. Zoller, Nature 404, 579 (2000) target pushing ion – solid state qubits (e.g. charge qubit) laser L. Tian et al., PRL 92, 247902 (2004) H. Häffner et al., IQOQI Innsbruck …more ideas …? 3. Quantum information processing with trapped Ca+ ions 2.1 Deutsch-Jozsa algorithm with a single Ca+ ion 2.2 Cirac-Zoller CNOT gate operation with two ions 2.3 Entanglement and Bell state generation 2.4 State tomography 2.5 Process tomography of the CNOT gate 2.6 Tripartite entanglement (W-states, GHZ-states) 2.7 Multipartite entanglement 3.0 Advanced Procedures and Operations 3.1 Teleportation 323.2 Entanglement Swapping 3.3 Metrology with entangled states 404.0 Scaling the ion trap quantum computer 4.1 More complex and faster procedures Scalable quantum computation requires error correction Toffoli gate: controlled-controlled NOT Toffoli gate (Tommaso Toffoli, 1980): …… is a universal reversible logic gate, i.e. any reversible circuit can be constructed from Toffoli gates. also known as the controlled-controlled-NOT or CCNOT-gate operation useful, e.g. for error correction Toffoli gate: pulse sequence use 2-phonon excitation Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009) B B B B B B B B B B C B B B C effective for n=1,2 result: n=1 iff SS undo encoding, reverse phases CNOT iff n=1 Toffoli gate: experimental truth table density matrix State Fidelity Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009) Toffoli gate: process tomography - matrix for ideal TOFFOLI gate operation III IIX IIY IIZ ZZZ IXI ZZZ III Toffoli gate: process tomography - matrix for the real TOFFOLI gate operation Mean Process Fidelity Th. Monz et al., Phys. Rev. Lett. 102, 040501 (2009) Quantum procedures and fidelities ► single qubit operations > 99 % ► 2-qubit CNOT gate ~ 93 % ► Bell states 93-95 % ► W and GHZ states 85-90 % ► Quantum teleportation 83 % ► Entanglement swapping ~ 80 % ► Toffoli gate operation 71 % BUT: for fault-tolerant operation needed > 99 % ! Mølmer - Sørensen gate - operation K. Mølmer, A. Sørensen, bichromatic laser excitation Phys. Rev. Lett. 82, 1971 (1999) close to upper and lower C. A. Sackett et al., sidebands induces collective Nature 404, 256 (2000) state changes (spin flips) Measuring entanglement C.
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