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Quantum Measurement and Bath Engineering for Superconducting Qubits Via Multiple Parametric Couplings

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Quantum Measurement and Bath Engineering for Superconducting Qubits Via Multiple Parametric Couplings Quantum measurement and bath engineering for superconducting qubits via multiple parametric couplings by Xi Cao Bachelor of Science, Wuhan University, 2014 Submitted to the Graduate Faculty of the Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2021 UNIVERSITY OF PITTSBURGH DIETRICH SCHOOL OF ARTS AND SCIENCES This dissertation was presented by Xi Cao It was defended on February 11, 2021 and approved by Michael Hatridge, Department of Physics and Astronomy, University of Pittsburgh David Pekker, Department of Physics and Astronomy, University of Pittsburgh Sergey Frolov, Department of Physics and Astronomy, University of Pittsburgh Ayres Freitas, Department of Physics and Astronomy, University of Pittsburgh Daniel Lambrecht, Department of Chemistry and Physics, Florida Gulf Coast University Dissertation Director: Michael Hatridge, Department of Physics and Astronomy, University of Pittsburgh ii Copyright © by Xi Cao 2021 iii Quantum measurement and bath engineering for superconducting qubits via multiple parametric couplings Xi Cao, PhD University of Pittsburgh, 2021 Quantum computers have huge potential applications, but do not currently exist. It has already been proven that a quantum computer would outperform the best classical supercomputers in certain problems, some of which have vital connections with our daily lives. For example, quantum computers efficiently solve the prime number factoring problem, which in turn is the foundation of the RSA algorithm behind most online transactions. There is a great deal of current effort to implement quantum computers, and we have seen good progress in platforms including superconducting circuits, ion traps, and photons in cavity QED systems and spins in semiconductors. These machines include up to roughly 50 quantum bits at present, but they are not very useful as quantum errors quickly decohere the computer's state and prevent computation. These errors can be mitigated via quantum error correction at the cost of additional size and complexity. Progress in the field towards error corrected, large-scale quantum machines requires us to require new tools for controlling, coupling, and reading out qubits. In this thesis, I will focus on such explorations in superconducting circuits. In this thesis, we seek to expand the already flexible toolkit of quantum circuits by exploring the uses of parametric couplings based on third-order nonlinearities. This type of nonlinearities has only been used in quantum-limited amplifiers before, here we try to further explore their applications by creating new methods for controlling and measuring qubits that based on it. In the first experiment, we address the problem of implementing a highly efficient quan- tum non-demolition qubit readout. With the use of two-mode squeezed (TMS) light and combined with phase-preserving parametric amplifiers into an interferometer for dispersive qubit readout, we demonstrate a measurement scheme with a 44% improvement in power signal-to-noise ratio. We also investigate the back-action of the measurement scheme. In the second experiment, we create an effective chemical potential for photons with parametric system-bath coupling. In particular, we use a lossy Superconducting Nonlinear iv Asymmetric Inductive eLement (SNAIL) as both the bath and coupler. The bath engineering is realized by combining the multiple parametric drives and the dissipation together. v Table of contents I. Introduction .................................... 1 A. Background of quantum computation . 1 B. History and challenges for superconducting quantum computation . 3 C. Quantum measurement and two-mode squeezed qubit readout . 7 D. A chemical potential for transmon qubits . 12 E. Organization of this thesis . 13 II. Hamiltonian engineering tool box ...................... 15 A. Overview . 15 B. Superconducting qubits and dispersive measurement . 15 C. Rotating wave approximation and parametric coupling . 24 D. The Josephson Parametric Converter . 28 E. Two-mode squeezed light generated from a JPC . 33 F. The Superconducting Nonlinear Asymmetric Inductive eLement . 36 G. Measurement back-action and weak measurement protocol . 40 III. Qubit measurement with two-mode squeezed light . 45 A. Overview . 45 B. Experimental setup . 46 1. Cryogenic setup . 46 2. Pump leakage cancellation . 48 C. Sample parameters . 52 D. Interference of two-mode squeezed light with JPC . 52 E. Qubit readout with two-mode squeezed vaccum . 56 F. SNR improvement with displaced two-mode squeezed vacuum . 58 G. Backaction of two-mode squeezed light measurement . 61 H. Conclusion . 67 IV. Qubit-bath engineering via parameteric drives: Theory . 69 vi A. Overview . 69 B. A parametrically generated chemical potential for light . 70 C. Bath engineering via a JPC with one low-frequency mode . 73 D. Bath engineering via lossy SNAIL . 76 1. System Hamiltonian . 76 2. Bath engineering with drive and dissipation of the system . 79 3. Master equation and numerical results . 84 E. Conclusion . 91 V. From Hamiltonian to microwave design ................... 92 A. Overview . 92 B. Black box quantization . 92 C. SNAIL coefficient calculation . 95 D. User's manual for BBQ . 96 VI. Qubit-bath engineering via parametric drive: Experiment ....... 98 A. Overview . 98 B. Low frequency JPC . 98 1. Transmission line based low-frequency JPC . 98 2. Lumped low-frequency JPC . 103 C. Qubit parametrically coupled to a lossy SNAIL . 107 1. Microwave design and fabrication of the sample . 107 2. Experiment setup . 115 3. Sample parameters . 115 4. Experiment results . 118 D. Conclusion and outlook . 128 VII. Conclusion ..................................... 129 Bibliography ....................................... 135 vii List of figures 1 Dispersive measurement ............................. 8 2 Schematics of squeezing states ......................... 10 3 Summary of transmon qubit .......................... 16 4 Summary of dispersive measurement ..................... 20 5 A child on a swing ................................. 25 6 Schematic of three-wave coupling ....................... 26 7 Summary of the Josephson Parametric Converter . 30 8 Gain and conversion process of a JPC .................... 32 9 Generation of two-mode squeezed light with JPC . 35 10 The SNAIL ..................................... 37 11 Applications of SNAILs ............................. 39 12 Bloch sphere representation of measurement back-action . 43 13 Pulse sequence for determining the measurement back-action . 44 14 Theory result for the measurement back-action . 44 15 Schematic of the TMS experiment setup ................... 47 16 Wiring diagram of the cryogenic microwave measurement setup . 49 17 Wiring diagram of room temperature setup for canceling the pump leakage ........................................ 50 18 Normalized signal strength of qubit readout with coherent light and displaced two-mode squeezed vacuum ..................... 51 19 Transmission measurement of the S parameter of the TMS interferom- eter as a function of the relative pump phase . 54 20 Two-mode squeezed vacuum .......................... 55 21 Qubit readout with two-mode squeezed vacuum . 57 22 Pulse sequence for quantifying the back action of noise measurement . 59 viii 23 SNR of qubit readout with coherent light and displaced two-mode squeezed vacuum. ................................. 60 24 Experiment data for back action of weak measurement .......... 63 25 Quantum efficiency obtained by analyzing the back-action of weak mea- surements ...................................... 64 26 Experiment data for z-axis back action of weak measurement ...... 65 27 Calculated overall efficiency as a function of NVR for different analyzer JPC/TMS interferometer efficiency ...................... 66 28 Schematics of the system parametrically couple to a thermal bath .. 71 29 Low frequency JPC implementation for bath engineering ........ 73 30 Schematic of a transmon qubit dispersively coupled to a lossy SNAIL 77 31 Schematics of `Σ drive' .............................. 81 32 Drive selectivity due to the qubit anharmonicity .............. 82 33 Schematics of `δ drive' .............................. 83 34 Schematics of ef control ............................. 84 35 Simulation results for natural decay ...................... 85 36 Simulation result for `Σge;s drive' ....................... 86 37 `Σge;s drive' Γge and Γeg vs pump strength ................... 87 38 Simulation result for `δge;s drive' ........................ 88 39 Simulation results for single and multiple parametric drives ....... 89 40 Kerr effect with δge;s drive ............................ 90 41 Schematic of black box quantization ...................... 93 42 Bandpass filter design for low frequency JPC ................ 100 43 Optical images of low frequency JPC ..................... 101 44 Optical images of the JRM ........................... 102 45 Phase data of the modes of the low frequency JPC ............ 103 46 Gain and conversion data for low frequency JPC ............. 104 47 Circuit schematic for lumped low frequency JPC ............. 105 48 3D model for lumped low frequency JPC in HFSS ............ 106 ix 49 Summary of the `three-mode' version with SNAIL and array low fre- quency resonator .................................. 108 50 Summary of the chemical potential with lossy SNAIL .......... 110 51 HFSS design of a qubit couple to a lossy SNAIL .............. 111 52 Im(Y ) from qubit lumped port ........................
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