Design, fabrication and test of a four superconducting quantum-bit processor Vivien Schmitt To cite this version: Vivien Schmitt. Design, fabrication and test of a four superconducting quantum-bit processor. Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. NNT : 2015PA066184. tel- 01214394 HAL Id: tel-01214394 https://tel.archives-ouvertes.fr/tel-01214394 Submitted on 12 Oct 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité : Physique École doctorale : « Physique en Île-de-France » réalisée dans le groupe Quantronique SPEC - CEA Saclay France présentée par Vivien SCHMITT pour obtenir le grade de : DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse : Design, fabrication and test of a four superconducting quantum-bit processor soutenue le 3 septembre 2015 devant le jury composé de : Dr. Olivier Buisson Rapporteur Pr. Alexey Ustinov Rapporteur Dr. Benjamin Huard Examinateur Pr. Frank K. Wilhelm Examinateur Dr. Denis Vion Membre invité Dr. Daniel Esteve Directeur de thèse Contents Contents 3 1 Introduction: the making of superconducting quantum pro- cessors 7 1.1 The origins of quantum computing ................ 7 1.1.1 From entanglement to quantum computing ....... 7 1.1.2 Blueprint(s) for a quantum processor ........... 8 1.1.3 Physical implementations of quantum bits ........ 9 1.2 State of the art of superconducting quantum processors . 9 1.2.1 Superconducting qubits .................. 9 1.2.2 The transmon qubit .................... 9 1.2.3 Superconducting quantum processors ........... 11 1.3 Operating the Grover search algorithm in a two-qubit processor 11 1.4 Towards a scalable superconducting quantum processor .... 13 1.4.1 A more scalable design ................... 13 1.4.2 Fabrication issues ...................... 13 1.4.3 Demonstrating multiplexed qubit readout ........ 14 1.4.4 Testing a 4-qubit processor ................ 16 2 Operating a transmon based two-qubit processor 19 2.1 Superconducting qubits based on Josephson junctions ..... 20 2.1.1 The Josephson junction .................. 20 2.1.2 The SQUID: a flux tunable Josephson junction ..... 21 2.1.3 The Cooper Pair Box ................... 22 2.1.4 Different Cooper pair box flavors . ........... 23 2.2 The transmon ............................ 24 2.2.1 Single qubit gates ..................... 25 2.2.1.1 Single qubit gates with resonant gate-charge microwavepulses ................ 25 2.2.1.2 Z rotations using phase driven gates ..... 26 2.2.2 Decoherence: relaxation and dephasing ......... 26 3 CONTENTS 4 2.2.2.1 Relaxation .................... 27 2.2.2.2 Pure dephasing .................. 29 2.2.3 Qubit state readout .................... 29 2.2.3.1 Cavity quantum electrodynamics . ..... 30 2.2.3.2 Linear dispersive readout ............ 31 2.2.3.3 The Josephson bifurcation amplifier . .... 32 2.2.3.4 Cavity induced relaxation and dephasing . 37 2.3 Processor operation ........................ 38 2.3.1 Two-qubit interaction yielding a universal gate ..... 40 2.3.2 Quantum state tomography ................ 43 2.4 Gate tomography .......................... 44 2.4.1 Quantum process tomography of the √iSW AP gate . 44 2.5 Running the Grover search quantum algorithm ......... 45 2.5.1 The Grover search algorithm ............... 46 2.5.2 Running the Grover search algorithm . ........ 47 3 Design of a 4 qubit processor 49 3.1 A N +1 line architecture . .................... 49 3.2 Single qubit gates .......................... 51 3.2.1 Z axis rotations . ..................... 51 3.2.2 X and Y axis rotations . .................. 52 3.2.2.1 Displacement induced phase .......... 53 3.2.2.2 Spurious drive on the other qubits ....... 53 3.2.2.3 Alternatives ................... 54 3.3 Two-qubits gates .......................... 54 3.3.1 Coupling with bus resonator ............... 54 3.3.2 iSwap gate ......................... 55 3.3.3 Validity of the empty bus approximation ........ 55 3.3.4 Residual coupling ..................... 55 3.4 Simultaneous readout of transmons ................ 56 3.4.1 Frequency multiplexing of readouts ............ 57 3.4.2 Amplification schemes for multiplexing .......... 57 3.4.2.1 Linear readout with a quantum limited ampli- fier........................ 57 3.4.2.2 Multiplexing several Josephson bifurcation am- plifiers ....................... 58 3.4.3 JBA characteristics ..................... 58 3.4.3.1 Choice of JBA parameters ........... 59 3.4.3.2 Qubit-readout coupling ............. 60 3.5 Processor Parameters ....................... 60 3.5.1 Final choice . ....................... 61 3.5.2 Overall decay and coherence rates ............ 61 3.6 Sample design ............................ 63 3.6.1 Overall design ....................... 63 3.6.2 Microwave simulations ................... 64 3.6.3 Transmission, admittance and impedance matrices . 66 CONTENTS 5 3.6.4 Extraction of the relevant parameters .......... 66 3.6.4.1 Qubit resonance width ............. 68 3.6.4.2 Qubit readout coupling constant ........ 68 3.7 Complete design .......................... 69 4 Sample fabrication 71 4.1 Fabrication of large structures using optical lithography .... 73 4.2 Fabrication of Josephson junctions and qubits ......... 75 4.3 Airbridge fabrication ........................ 78 4.4 Cutting and mounting ....................... 81 5 Multiplexed readout of transmon qubits 85 5.1 Sample and experimental setup ................. 85 5.1.1 Sample ........................... 85 5.1.2 Low temperature setup . ................. 86 5.1.3 Microwave setup ...................... 86 5.2 Experimental techniques ...................... 86 5.2.1 Single sideband mixing ................... 86 5.2.2 Demodulation and horizontal synchronization ...... 90 5.3 Sample characterization ...................... 91 5.3.1 JBA readout resonator characterization ......... 91 5.3.2 Qubit spectroscopy ..................... 94 5.3.3 Qubit-readout resonator coupling constant . ..... 94 5.4 Single qubit readout ........................ 95 5.5 Multiplexed qubits readout .................... 103 5.5.1 Readout frequencies, signal generation and analysis . 103 5.5.2 Switching performance ................... 105 5.5.3 Simultaneous qubit drive and readout .......... 106 5.5.4 Readout crosstalk between JBAs ............. 107 5.6 Overall performance and conclusion ............... 109 6 Characterizinga4qubitprocessor prototype: preliminary results 111 6.1 Sample and experiment setup ................... 111 6.1.1 Sample ........................... 111 6.1.2 Low temperature setup . ................. 112 6.1.3 Microwave setup ...................... 114 6.2 Individual cell characterization . ................. 114 6.2.1 JBA resonator characterization .............. 114 6.2.1.1 S21 coefficient varying with power ....... 114 6.2.1.2 Quality factor in the low power linear regime . 115 6.2.1.3 Readout contrast ................. 116 6.2.2 Qubit characterization . ................. 118 6.2.2.1 Spectroscopy ................... 118 6.2.2.2 Single qubit gates: Rabi oscillations ...... 119 6.2.2.3 Qubit relaxation and dephasing times ..... 120 CONTENTS 6 6.2.3 Frequency control, flux lines crosstalk .......... 121 6.3 Bus characterization and coupling to the qubits ......... 122 6.4 Qubit-qubit bus mediated interaction ............... 127 6.4.1 Resonance condition for qubit-qubit swapping ...... 127 6.4.2 Swapping coupling strength . .............. 129 6.4.3 Bus mediated swap ..................... 132 6.4.4 Simulation of the swap experiments ........... 134 6.5 Conclusion ............................. 134 7 Conclusion and perspectives 137 7.1 Operating the 4-qubit processor .................. 137 7.2 Scalability issues faced by superconducting processors ..... 138 7.2.1 The readout scalability issue ............... 138 7.2.2 All scalability issues .................... 139 7.3 Other promising strategies for quantum information processing 140 7.3.1 The hybrid route ..................... 140 7.3.2 Semiconductor qubits are back .............. 141 7.4 Personal viewpoint . ....................... 141 A Numerical simulation of the switching dynamics of a JBA 143 A.1 Equivalent model of the JBA resonator . ............ 143 A.2 Equation of motion of the JBA .................. 145 A.3 Simulations ............................. 146 Bibliography 149 Chapter 1 Introduction: the making of superconducting quantum processors The research reported in this thesis deals with the design, the fabrication and the test of superconducting processors with the aim of running, on simple cases, quantum codes overcoming classical ones. 1.1 The origins of quantum computing 1.1.1 From entanglement to quantum computing The strong interest for quantum information dates back to the experimental demonstration of the violation of Bell inequalities in the early 1980s (see [1] and references therein to earlier work). These experiments shed light on the concept of entangled state first considered by Einstein, Podolski and Rosen when establishing their paradox [2]. An entangled