High fidelity readout and protection of a 43Ca+ trapped ion qubit

High Fidelity Readout and Protection of a 43Ca+ Trapped Ion Qubit A thesis submitted for the degree of Doctor of Philosophy Trinity Term 2009 David Szwer St. Catherine’s College, Oxford This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca+ ions for quantum information processing. I present a rate equations model of 43Ca+, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca+ and a 43Ca+ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of π-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n + 1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magneticfield-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.

[1]  Timothy C. Ralph,et al.  Efficient Toffoli gates using qudits , 2007 .

[2]  C. S. Wood,et al.  Deterministic Entanglement of Two Trapped Ions , 1998 .

[3]  M. Hohenstatt,et al.  "Optical-sideband Cooling of Visible Atom Cloud Confined in Parabolic Well" , 1978 .

[4]  Ray Freeman,et al.  Spin Choreography: Basic Steps in High Resolution NMR , 1996 .

[5]  Wineland,et al.  Laser-cooling limits and single-ion spectroscopy. , 1987, Physical review. A, General physics.

[6]  C. Monroe,et al.  Experimental entanglement of four particles , 2000, Nature.

[7]  Van Dyck,et al.  New high-precision comparison of electron and positron g factors. , 1987, Physical review letters.

[8]  A. Steane,et al.  Long-lived mesoscopic entanglement outside the Lamb-Dicke regime. , 2006, Physical review letters.

[9]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  Michael J Biercuk,et al.  Optimized noise filtration through dynamical decoupling. , 2009, Physical review letters.

[11]  Frequency metrology on the 4s(2)S(1/2)-4p(2)P(1/2) transition in Ca-40(+) for a comparison with quasar data , 2008, 0804.4130.

[12]  L. Deslauriers,et al.  T-junction ion trap array for two-dimensional ion shuttling, storage, and manipulation , 2005, quant-ph/0508097.

[13]  R. D. Cowan,et al.  The Theory of Atomic Structure and Spectra , 1981 .

[14]  M. Hohenstatt,et al.  Localized visible Ba + mono-ion oscillator , 1980 .

[15]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[16]  Sankey,et al.  Quantum jumps and the single trapped barium ion: Determination of collisional quenching rates for the 5d2D5/2 level. , 1990, Physical Review A. Atomic, Molecular, and Optical Physics.

[17]  Fortson.  Possibility of measuring parity nonconservation with a single trapped atomic ion. , 1993, Physical review letters.

[18]  D. Leibfried,et al.  Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate , 2003, Nature.

[19]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

[20]  D. M. Lucas,et al.  Scalable simultaneous multiqubit readout with 99.99% single-shot fidelity , 2009, 0906.3304.

[21]  R. Schuch,et al.  SMILETRAP—A Penning trap facility for precision mass measurements using highly charged ions , 2002 .

[22]  X Wang,et al.  Multibit gates for quantum computing. , 2001, Physical review letters.

[23]  Klaus Molmer,et al.  Entanglement and quantum computation with ions in thermal motion , 2000 .

[24]  R. Blatt,et al.  Precision measurement of the branching fractions of the 4p 2P3/2 decay of Ca II , 2008, 0807.2905.

[25]  C. F. Roos,et al.  Nonlinear coupling of continuous variables at the single quantum level , 2008 .

[26]  Karen J. Olsen,et al.  NIST Atomic Spectra Database (version 2.0) , 1999 .

[27]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[28]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[29]  J. Stacey.  Stabilization and control in a linear ion trap , 2003 .

[30]  Crystallization of Ca + ions in a linear rf octupole ion trap , 2007 .

[31]  J. O'Brien.  Optical Quantum Computing , 2007, Science.

[32]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[33]  S. Olmschenk,et al.  Quantum Teleportation Between Distant Matter Qubits , 2009, Science.

[34]  D. Leibfried.  INDIVIDUAL ADDRESSING AND STATE READOUT OF TRAPPED IONS UTILIZING RF MICROMOTION , 1999 .

[35]  S. A. van den Berg,et al.  Direct frequency comb spectroscopy of trapped ions , 2008, CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference.

[36]  W C Griffith,et al.  New limit on the permanent electric dipole moment of 199Hg. , 2000, Physical review letters.

[37]  Andrew M. Steane,et al.  How to build a 300 bit, 1 Giga-operation quantum computer , 2004, Quantum Inf. Comput..

[38]  G. Werth,et al.  Precise determination of the ground state hyperfine structure splitting of43Ca II , 1994 .

[39]  M. G. Boshier,et al.  Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems , 2002 .

[40]  D. James,et al.  Scalable, high-speed measurement-based quantum computer using trapped ions. , 2008, Physical review letters.

[41]  C. Monroe,et al.  Scaling and suppression of anomalous heating in ion traps. , 2006, Physical review letters.

[42]  Gang Shu,et al.  Precision measurement of the branching ratio in the 6P3/2 decay of BaII with a single trapped ion , 2008, 0804.4173.

[43]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[44]  T. Monz,et al.  Process tomography of ion trap quantum gates. , 2006, Physical review letters.

[45]  Christopher R. Monroe,et al.  Near-perfect simultaneous measurement of a qubit register , 2006, Quantum Inf. Comput..

[46]  J M Amini,et al.  High-fidelity transport of trapped-ion qubits through an X-junction trap array. , 2009, Physical review letters.

[47]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[48]  W. Paul,et al.  Das elektrische Massenfilter , 1955 .

[49]  R. Prevedel,et al.  High-speed linear optics quantum computing using active feed-forward , 2007, Nature.

[50]  R. Blatt,et al.  Towards fault-tolerant quantum computing with trapped ions , 2008, 0803.2798.

[51]  Universal Quantum Simulators: Correction , 1998, Science.

[52]  I. Chuang,et al.  Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.

[53]  S Das Sarma,et al.  Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem. , 2007, Physical review letters.

[54]  G. Uhrig,et al.  Exact results on dynamical decoupling by π pulses in quantum information processes , 2008 .

[55]  Erich Novak.  Quantum Complexity of Integration , 2001, J. Complex..

[56]  Norman F. Ramsey,et al.  A New Molecular Beam Resonance Method , 1949 .

[57]  L. DiCarlo,et al.  Demonstration of two-qubit algorithms with a superconducting quantum processor , 2009, Nature.

[58]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[59]  T. Schaetz,et al.  Simulating a quantum magnet with trapped ions , 2008 .

[60]  D. Wineland,et al.  Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place , 2008, Science.

[61]  Seth Lloyd,et al.  Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation , 2008, SIAM Rev..

[62]  R. Raussendorf,et al.  A fault-tolerant one-way quantum computer , 2005, quant-ph/0510135.

[63]  Isaac L. Chuang,et al.  Individual addressing of ions using magnetic field gradients in a surface-electrode ion trap , 2008, 0811.2422.

[64]  L-M Duan,et al.  Phase control of trapped ion quantum gates , 2005 .

[65]  H. Briegel,et al.  Measurement-based quantum computation , 2009, 0910.1116.

[66]  R. Timmermans,et al.  Atomic parity nonconservation in Ra , 2008 .

[67]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[68]  D. M. Lucas,et al.  Implementation of a symmetric surface-electrode ion trap with field compensation using a modulated Raman effect , 2009, 0909.3272.

[69]  Michael J. Biercuk,et al.  Experimental Uhrig Dynamical Decoupling using Trapped Ions , 2009, 0902.2957.

[70]  Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and the determination of atomic dipole matrix elements , 2008, 0808.1826.

[71]  G. Gabrielse.  Antiproton mass measurements , 2006 .

[72]  C. F. Roos,et al.  ‘Designer atoms’ for quantum metrology , 2006, Nature.

[73]  E. Knill,et al.  Realization of quantum error correction , 2004, Nature.

[74]  D. Wineland,et al.  High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements. , 2007, Physical review letters.

[75]  J. Benhelm.  Precision Spectroscopy and Quantum Information Processing with Trapped Calcium Ions , 2008 .

[76]  T. Dent,et al.  Competing bounds on the present-day time variation of fundamental constants , 2008, 0812.4130.

[77]  M. Nieto,et al.  Coherent States and the Forced Quantum Oscillator , 1965 .

[78]  N. Badnell,et al.  Atomic data from the IRON project. LXIV. Radiative transition rates and collision strengths for Ca II , 2007, 0704.3807.

[79]  A. Zeilinger,et al.  Experimental one-way quantum computing , 2005, Nature.

[80]  Lov K. Grover,et al.  Preserving quantum states using inverting pulses: a super-Zeno effect. , 2006, Physical review letters.

[81]  D. Wineland,et al.  A 303-MHz frequency standard based on trapped Be/sup +/ ions , 1991, IEEE Transactions on Instrumentation and Measurement.

[82]  D. DiVincenzo,et al.  The Physical Implementation of Quantum Computation , 2000, quant-ph/0002077.

[83]  G. Gabrielse,et al.  New measurement of the electron magnetic moment and the fine structure constant. , 2006, Physical review letters.

[84]  C. F. Roos,et al.  High-fidelity ion-trap quantum computing with hyperfine clock states , 2007 .

[85]  D. Dieks.  Communication by EPR devices , 1982 .

[86]  Steven Chu,et al.  Precision measurement of ℏ/mCs based on photon recoil using laser-cooled atoms and atomic interferometry , 1994 .

[87]  O. Gühne,et al.  03 21 7 2 3 M ar 2 00 6 Scalable multi-particle entanglement of trapped ions , 2006 .

[88]  R. B. Blakestad,et al.  Creation of a six-atom ‘Schrödinger cat’ state , 2005, Nature.

[89]  Michael J. Biercuk,et al.  Optimized dynamical decoupling in a model quantum memory , 2008, Nature.

[90]  R. Feynman.  Simulating physics with computers , 1999 .

[91]  F. Schmidt-Kaler,et al.  Quantum computing with trapped ions , 2008, 0809.4368.

[92]  Jon H. Shirley,et al.  NIST cesium fountains: current status and future prospects , 2007, SPIE Optical Engineering + Applications.

[93]  P. Baird.  Parity Non-Conservation in Atomic Bismuth , 1979 .

[94]  N. Timoney,et al.  Individual addressing of trapped ions and coupling of motional and spin states using RF radiation. , 2007, Physical review letters.

[95]  F. Schmidt-Kaler,et al.  Robust state preparation of a single trapped ion by adiabatic passage , 2005, quant-ph/0508159.

[96]  J. P. Home,et al.  Isotope-selective photoionization for calcium ion trapping , 2004 .

[97]  J. P. Home,et al.  Memory coherence of a sympathetically cooled trapped-ion qubit , 2008, 0810.1036.

[98]  P. C. Haljan,et al.  Entanglement of trapped-ion clock states , 2005 .

[99]  W. Paul.  Electromagnetic traps for charged and neutral particles , 1990 .

[100]  S. Das Sarma,et al.  How to Enhance Dephasing Time in Superconducting Qubits , 2007, 0712.2225.

[101]  S. Olmschenk,et al.  Manipulation and detection of a trapped Yb+ hyperfine qubit , 2007, 0708.0657.

[102]  F. Mintert,et al.  Ion-trap quantum logic using long-wavelength radiation. , 2001, Physical review letters.

[103]  G. Imreh.  Implementing segmented ion trap designs for quantum computing , 2008 .

[104]  M. A. Rowe,et al.  Heating of trapped ions from the quantum ground state , 2000 .

[105]  G. K. Woodgate.  Elementary Atomic Structure , 1970 .

[106]  D. M. Lucas,et al.  Precision Measurement of the Lifetime of the 3d 2 D 5/2 state in 40 Ca + , 2000 .

[107]  G. Uhrig.  Keeping a quantum bit alive by optimized pi-pulse sequences. , 2006, Physical review letters.

[108]  S. Lloyd,et al.  DYNAMICAL SUPPRESSION OF DECOHERENCE IN TWO-STATE QUANTUM SYSTEMS , 1998, quant-ph/9803057.

[109]  B. Blinov,et al.  Barium ions for quantum computation , 2009, 0905.2701.

[110]  D Hayes,et al.  Heralded quantum gate between remote quantum memories. , 2009, Physical review letters.

[111]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[112]  William D. Langer,et al.  A measurement of the hyperfine structure of C17O , 1981 .

[113]  Gerard J. Milburn,et al.  Ion Trap Quantum Computing with Warm Ions , 2000 .

[114]  P. Gill.  Optical frequency standards , 2005 .

[115]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[116]  M. Freedman,et al.  Topological Quantum Computation , 2001, quant-ph/0101025.

[117]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[118]  M D Barrett,et al.  Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System , 2005, Science.

[119]  D M Lucas,et al.  High-fidelity readout of trapped-ion qubits. , 2008, Physical review letters.

[120]  Sandberg,et al.  Shelved optical electron amplifier: Observation of quantum jumps. , 1986, Physical review letters.

[121]  C. F. Roos,et al.  Quantum teleportation with atoms: quantum process tomography , 2007, 0704.2027.

[122]  A. Steane,et al.  A long-lived memory qubit on a low-decoherence quantum bus , 2007, 0710.4421.