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Optimization of Superconducting Flux Qubit Readout Using Near-Quantum-Limited Amplifiers by Jedediah Edward Jensen Johnson A

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Optimization of Superconducting Flux Qubit Readout Using Near-Quantum-Limited Amplifiers by Jedediah Edward Jensen Johnson A Optimization of superconducting flux qubit readout using near-quantum-limited amplifiers by Jedediah Edward Jensen Johnson A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor John Clarke, Chair Professor Irfan Siddiqi Professor Theodore Van Duzer Fall 2012 Optimization of superconducting flux qubit readout using near-quantum-limited amplifiers Copyright 2012 by Jedediah Edward Jensen Johnson 1 Abstract Optimization of superconducting flux qubit readout using near-quantum-limited amplifiers by Jedediah Edward Jensen Johnson Doctor of Philosophy in Physics University of California, Berkeley Professor John Clarke, Chair Though superconducting qubits offer the potential for a scalable quantum computing ar- chitecture, the high-fidelity readout necessary to execute practical algorithms has thus far remained elusive. Moreover, achievements toward high fidelity have been accompanied by either long measurement times or demolition of the quantum state. In this dissertation, we address these issues with the novel integration of two ultralow-noise, superconducting am- plifiers into separate dispersive flux qubit measurements. We first demonstrate a flux qubit inductively coupled to a 1.294-GHz nonlinear oscillator formed by a capacitively shunted DC SQUID. The frequency of the oscillator is modulated by the state of the qubit and is detected via microwave reflectometry. A microstrip SQUID (Superconducting QUantum Interference Device) amplifier (MSA) is used to increase the sensitivity of the measurement over that of a semiconductor amplifier. In the second experiment, we report measurements of a flux qubit coupled via a shared inductance to a quasi-lumped element 5.78-GHz readout res- onator formed by the parallel combination of an interdigitated capacitor and a meander line inductor. The system noise is substantially reduced by a near-quantum-limited Josephson parametric amplifier (paramp). We present measurements of increased fidelity and reduced measurement backaction using the MSA at readout excitation levels as low as one hundredth of a photon in the readout resonator, observing a 4.5-fold increase in the readout visibility. Furthermore, at low readout excitation levels below one tenth of a photon in the readout resonator, no reduction in T1 is observed, potentially enabling continuous monitoring of the qubit state. Using the paramp, we demonstrate a continuous, high-fidelity readout with sufficient bandwidth and signal-to- noise ratio to resolve quantum jumps in the flux qubit. This is enabled by a readout which discriminates between the readout pointer state distributions to an error below one part in 1000. This, along with the ability to make many successive readouts in a time T1, permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This method enables us to eliminate errors due to spurious thermal population, increasing the fidelity to 93.9%. Finally, we use heralding to introduce a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation. i Contents Contents i List of Figures iv List of Tables vii 1 Introduction 1 1.1 Quantum information . 2 1.2 Challenges of quantum computing . 3 1.3 Superconductivity . 3 1.3.1 Flux quantization . 3 1.3.2 Josephson junctions . 4 1.4 Superconducting Quantum Interference Device . 7 1.5 Superconducting qubits . 9 1.6 Scope of research . 11 2 Superconducting flux qubits 13 2.1 The one-junction flux qubit . 13 2.2 The three-junction flux qubit . 15 2.3 The four-junction flux qubit . 19 2.4 Energy level calculation for the three-junction qubit . 22 2.5 Qubit control and measurement schemes . 25 3 Readout and amplification 27 3.1 Dispersive measurement . 27 3.1.1 Jaynes-Cummings formulation of a flux qubit . 27 3.1.2 SQUID resonator . 30 3.1.3 Readout signal and noise . 31 3.2 Signal amplification . 34 3.3 Microstrip SQUID amplifier . 38 3.4 Josephson parametric amplifier . 41 4 Design and fabrication of devices 47 ii 4.1 Flux qubits . 47 4.1.1 Qubit design . 48 4.1.2 Resist stack . 49 4.1.3 Electron beam lithography . 50 4.1.4 Aluminum deposition . 52 4.1.5 Oxygen plasma . 53 4.1.6 Overlap capacitors . 56 4.1.7 Device screening . 56 4.1.8 Device layouts and parameters . 58 4.2 Microstrip SQUID amplifier . 62 4.2.1 Previous work . 63 4.2.2 Input coil . 64 4.2.3 Junction process . 65 4.3 Josephson parametric amplifier . 65 5 Measurement infrastructure 67 5.1 Sample boxes . 67 5.2 Dilution refrigerator . 69 5.3 DC bias circuitry . 70 5.4 Microwave circuitry . 74 5.4.1 Coaxial lines and attenuation . 74 5.4.2 Cryogenic setup . 75 5.4.3 Room temperature measurement setup . 79 5.4.4 Data acquisition . 83 6 Qubit and amplifier characterization 84 6.1 Resonator characterization . 84 6.2 Flux qubit - resonator interaction . 85 6.3 Qubit spectroscopy . 87 6.4 Time domain characterization . 90 6.5 Amplifier performance . 94 6.5.1 System noise measurements . 94 6.5.2 MSA . 96 6.5.3 Paramp . 98 7 Fidelity and backaction measurements 100 7.1 SQUID resonator . 101 7.1.1 Pulse sequence . 101 7.1.2 Signal processing . 102 7.1.3 Readout improvement with MSA . 104 7.2 Circuit QED . 109 7.2.1 Quantum jumps . 109 iii 7.2.2 Fidelity measurements . 111 7.2.3 Readout pointer state discrimination . 113 7.2.4 Heralded state preparation . 114 7.2.5 Fidelity loss and readout backaction . 116 7.2.6 Fast qubit reset . 119 8 Conclusions 120 8.1 Summary of results . 120 8.2 Future directions . 121 Bibliography 122 iv List of Figures 1.1 RCSJ model and washboard potential of a Josephson junction. 6 1.2 SQUID schematic and critical current modulation vs flux. 8 1.3 SQUID current-voltage characteristics and voltage modulation vs flux. 9 1.4 A variety of superconducting qubits. 11 2.1 Double-well potential energy of the one junction flux qubit. 14 2.2 Schematic of the three junction flux qubit. 16 2.3 Surfaces of constant potential energy in the three junction flux qubit. 17 2.4 Potential energy slice of a three junction flux qubit with δt = 0. 19 2.5 Potential energy of a three junction flux qubit with non-negligible βq. 20 2.6 Potential advantages of the four junction flux qubit. 21 2.7 Flux qubit energy spectrum vs flux. 23 2.8 A sampling of flux qubit readout architectures. 26 3.1 Comparison of cavity and circuit QED. 28 3.2 Coupling of cQED readout cavity to external circuitry. 31 3.3 The dispersive qubit shift in a microwave resonator. 32 3.4 Readout pointer state vectors and noise in the IQ plane. 33 3.5 Simplified model of a generic amplifier. 34 3.6 Signal and noise amplification. 37 3.7 MSA overview. 39 3.8 Schematic representation of the paramp. 41 3.9 Response of the driven nonlinear oscillator. 43 3.10 Resonance frequency response with increasing power in a nonlinear oscillator. 43 3.11 Principles of phase-sensitive amplification in the paramp. 45 4.1 Headway PWM32 spinner. 48 4.2 Equipment for electron beam lithography. 50 4.3 Features patterned into electron beam resist. 51 4.4 Aluminum evaporators. 52 4.5 SEM images of Josephson junctions. 54 4.6 Double-angle shadow evaporation. 55 v 4.7 Probe station and desiccator. 57 4.8 False color optical micrograph of the SQUID resonator device. 58 4.9 False color SEM micrograph of the circuit QED device. 60 4.10 Optical photograph of the MSA with magnified inset of the junction region. 62 4.11 Niobium/aluminum sputtering system including argon ion mill. 64 4.12 Images of a Josephson parametric amplifier. 66 5.1 Flux qubit sample box for SQUID resonator readout. 68 5.2 Flux qubit sample box for circuit QED readout. 69 5.3 MSA cylindrical can and cryoperm shield. 70 5.4 Paramp launch and shielding. ..
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