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High Fidelity Readout of Trapped Ion Qubits

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High Fidelity Readout of Trapped Ion Qubits High Fidelity Readout of Trapped Ion Qubits A thesis submitted for the degree of Doctor of Philosophy Alice Heather Burrell Trinity Term Exeter College 2010 Oxford ii Abstract High Fidelity Readout of Trapped Ion Qubits A thesis submitted for the degree of Doctor of Philosophy, Trinity Term 2010 Alice Heather Burrell Exeter College, Oxford This thesis describes experimental demonstrations of high-fidelity readout of trapped ion quantum bits (“qubits”) for quantum information processing. We present direct single-shot measurement of an “optical” qubit stored in a single 40Ca+ ion by the process of resonance fluorescence with a fidelity of 99.991(1)% (sur- passing the level necessary for fault-tolerant quantum computation). A time-resolved maximum likelihood method is used to discriminate efficiently between the two qubit states based on photon-counting information, even in the presence of qubit decay from one state to the other. It also screens out errors due to cosmic ray events in the detec- tor, a phenomenon investigated in this work. An adaptive method allows the 99.99% level to be reached in 145 µs average detection time. The readout fidelity is asymmetric: 99.9998% is possible for the “bright” qubit state, while retaining 99.98% for the “dark” state. This asymmetry could be exploited in quantum error correction (by encoding the “no-error” syndrome of the ancilla qubits in the “bright” state), as could the likelihood values computed (which quantify confidence in the measurement outcome). We then extend the work to parallel readout of a four-ion string using a CCD camera and achieve the same 99.99% net fidelity, limited by qubit decay in the 400 µs exposure time. The behaviour of the camera is characterised by fitting experimental data with a model. The additional readout error due to cross-talk between ion images on the CCD is measured in an experiment designed to remove the effect of qubit decay; a spatial maximum likelihood technique is used to reduce this error to only 0.2(1) 10 4 per × − qubit, despite the presence of 4% optical cross-talk between neighbouring qubits. ≈ Studies of the cross-talk indicate that the readout method would scale with negligible loss of fidelity to parallel readout of 10 000 qubits with a readout time of 3 µs per ∼ ∼ qubit. Monte-Carlo simulations of the readout process are presented for comparison with experimental data; these are also used to explore the parameter space associated with fluorescence detection and to optimise experimental and analysis parameters. Applications of the analysis methods to readout of other atomic and solid-state qubits are discussed. iii iv ABSTRACT Acknowledgements I am extremely grateful to my supervisor Dr David Lucas who has collaborated with me on the readout work presented in this thesis. He has provided me with invaluable help and guidance during my time at Oxford, and I would also like to thank him for his enthusiasm and helpful comments and suggestions while proof-reading this thesis. I would also like to thank Professors Andrew Steane and Derek Stacey for all their advice, on both matters of research and of teaching. I am also grateful to Derek Stacey for comments on chapters 3 and 4. I feel very fortunate to have had the guidance of three such inspirational mentors during my time at Oxford. This thesis would not have been possible without the work of all the members of the Oxford ion-trap group who have built the experiment up to what it is today. I would like to thank both past group members and also those who I have had the pleasure of working with since I joined the group;- Dr. Jonathan Home, Dr. Nicholas Thomas, Dr. Eoin Phillips, Dr. Ben Keitch, Dr. Gergely Imreh, Dr. Simon Webster, Dr. Jeff Sherman, Dr. David Szwer, Dr. Michael (Spike W.) Curtis, David Allcock, Norbert Linke and more recently Tom Harty and Hugo Janacek. Thank you all for the advice and for conversation over tea. In particular I would like to mention David Szwer who has also collaborated with me on readout work: his work on readout in 43Ca+ is mentioned in this thesis and I am grateful for his help with apparatus descriptions (his thesis is copiously referenced in chapter 2). I worked with Norbert Linke and Jeff Sherman on assembly of the gold- on-alumina MicroTrap (“Serious Microtrap Business”); I would also like to thank Paul Pattinson and Peter Clack for technical assistance on this project. Thanks also go to Graham Quelch for technical assistance, and to Rob Harris and all of the team in the research workshop for help and advice with machine work. I am grateful to Andor for the loan of a “demo” camera, with which a large quantity of data in this thesis was taken. Thanks are due to Dominic Ford and Ross Church for writing and providing support for the PyXPlot plotting package which produced most of the graphs in this thesis. Finally, I thank my husband Christian, and my family and friends for all their love, encouragement and support throughout. v vi ACKNOWLEDGEMENTS Contents Abstract iii Acknowledgements v 1 Introduction 1 1.1 Quantum computation in ion traps . 1 1.1.1 Fidelity and speed of computation . 8 1.1.2 Otherprogresswithtrappedions . 8 1.2 Qubit readout in other architectures . 10 1.2.1 Neutralatoms ............................ 11 1.2.2 Superconductingqubits . 12 1.2.3 Quantumdots ............................ 16 1.2.4 Atomic impurities in semiconductors . 18 1.2.5 Rare-earth ions in solid-state hosts . 19 1.2.6 Linear optics/photonics . 20 1.2.7 NMR ................................. 21 1.3 Structureofthisthesis. 22 2 Apparatus 27 2.1 LinearPaultrap ............................... 27 2.2 Calcium.................................... 30 2.3 Lasers ..................................... 32 2.4 Imagingsystem................................ 35 2.4.1 ImagingsystemA .......................... 36 2.4.2 ImagingsystemB .......................... 37 2.4.3 ImagingsystemC .......................... 38 2.5 Experimentalcontrol. .. .. .. .. .. .. .. .. 42 2.5.1 Photoncounting ........................... 43 3 Ion readout by time-resolved photon counting 47 3.1 Readoutofqubitsincalcium . 47 3.1.1 40Ca+ Opticalqubit ......................... 47 3.1.2 40Ca+ Zeemanlevelqubit ...................... 49 3.1.3 43Ca+ hyperfinequbit ........................ 50 3.2 Analysistechniques.. .. .. .. .. .. .. .. .. 52 3.2.1 Quantifyingthereadouterror . 52 3.2.2 Thresholdmethod .......................... 53 3.2.3 Maximum likelihood method . 57 3.2.4 Adaptive maximum likelihood method . 60 3.3 Simulations .................................. 63 3.3.1 Justifications for analysis approximations . ..... 64 3.3.2 Sensitivity to analysis parameters . 68 vii viii CONTENTS 3.3.3 Dependence of error on experimental parameters . 69 3.4 Conclusions for photon counting readout . ..... 76 4 Time-resolved photon counting experiments 77 4.1 Investigating non-Poissonian dark counts . ....... 77 4.2 Ionreadoutexperimentalmethods . 82 4.3 Accounting for systematic errors . 86 4.3.1 Imperfect population preparation . 86 4.3.2 Darktobrighttransitions . 88 4.3.3 Brighttodarktransitions . 89 4.4 Resultsandanalysis ............................. 95 4.4.1 Thresholdmethod .......................... 96 4.4.2 Maximum likelihood method . 97 4.4.3 Adaptive maximum likelihood method . 101 4.5 Comparison with double measurement schemes . 102 4.6 Summary of experimental readout results . 108 5 Ion readout using a CCD camera 111 5.1 EMCCDcameras............................... 111 5.1.1 Noisesourcesinthecamera . 113 5.1.2 Comparison with other detectors . 116 5.1.3 Count distributions from the camera . 118 5.2 Analysistechniques.. .. .. .. .. .. .. .. .. 122 5.2.1 Selecting a “region-of-interest” in an image . 122 5.2.2 Single exposure: spatial resolution . 123 5.2.3 Multiple exposures: spatial and temporal resolution ....... 126 5.2.4 Extension to multiple ion readout . 129 5.2.5 Quantifyingthereadouterror . 132 5.3 Simulationmethods ............................. 133 5.3.1 Obtaining thresholds from simulated distributions . ....... 133 5.3.2 Monte-Carlo simulations . 135 6 CCD readout experiments 137 6.1 Experimentalmethods ............................ 137 6.1.1 Characterisation of camera properties . 140 6.2 Single qubit, single exposure experiment . 142 6.3 Single qubit, multiple exposure experiment . 147 6.4 Four ion “qunybble” experiment, single exposure . ....... 151 6.5 Simulations .................................. 158 6.5.1 Changing cross-talk (ion separation) . 159 6.5.2 Spatial resolution on the CCD . 160 6.5.3 Discussion of photon arrival rates and exposure times . 165 6.5.4 The EMCCD in photon-counting mode . 166 6.5.5 Imagingionsinasurfacetrap. 167 6.6 ConclusionsforEMCCDreadout . 169 7 Conclusion 175 7.1 Scalablereadoutoftrappedions . 175 7.1.1 Towards a large-scale architecture . 176 7.2 Application of methods to other ions . 178 7.2.1 Direct readout of an optical qubit . 179 7.2.2 Readoutofhyperfinequbits . 180 7.3 Application of methods to other systems . 185 CONTENTS ix 7.3.1 Neutralatoms ............................ 185 7.3.2 Superconductingqubits . 185 7.3.3 Quantumdots ............................ 186 7.3.4 Atomic impurities in semiconductors . 186 7.4 Measurement-based quantum computation . 186 7.5 Finalremarks................................. 187 A Monte-Carlo Simulation Code 189 B Photon counting publication 191 C CCD camera publication 197 x CONTENTS Chapter 1 Introduction 1.1 Quantum computation in ion traps The smallest unit of classical information is a “bit” which can have the value 0 or 1. It could perhaps represent the answer to a simple true-or-false question. We can encode much more complicated information in this binary representation, and indeed this is how information is stored in a classical computer. Computations proceed by operating on the bits with a succession of logic gates. Such gates may, for example, flip the state of a bit dependent on the state of a different “control” bit. After the computational sequence has finished, we can examine the states of the bits to see how the information contained within them has changed. These computations proceed according to classical laws of physics. Nature has provided a much more powerful way to represent information: as quan- tum bits, or “qubits”.
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