Nonlinear Dispersive Measurement with Superconducting Circuits

D. Sank, Roberto Collins, Evan R. Jeffrey +5 more

Yi Yin, Haohua Wang, M. Mariantoni +10 more

Mostafa Khezri, D. Sank, Zijun Chen +22 more

Irfan A. Siddiqi, Rajamani Vijay, Michael Metcalfe +4 more

The ``quantronium'' is a superconducting qubit consisting of a split Cooper pair box in which a large tunnel junction is inserted. This circuit has a special bias point where the Larmor frequency is, to first order, insensitive to fluctuations in the bias parameters---the charge of the box island and the phase of the large junction. At this optimal working point, the state of the qubit can be determined by dispersive measurements that probe the second derivative of the state energy with respect to these bias parameters. We use the quantronium phase degree of freedom to perform a nonlinear, dispersive measurement of its inductive response using bifurcation amplification. This dispersive readout projects the state of the qubit in a few nanoseconds, and its latching property allows us to record the resulting information in a few hundred nanoseconds. We have measured, using this technique, Rabi oscillations and Ramsey fringes with an improved signal-to-noise ratio and contrast. The speed of this readout scheme also opens the door for a class of experiments that would characterize the relaxation processes associated with the measurement protocol.

Marric Stephens

Mostafa Khezri

Quantum computers have the capability to improve the efficiency and speed of many computational tasks. Among different candidates for physical implementation of quantum bits (qubits), superconducting qubits are currently one of the most promising candidates due to their accessible fabrication process and recent rapid developments. Measurement of these qubits is usually done in a circuit quantum electrodynamics (QED) setup, for which experimental and theoretical research is conducted to improve the accuracy and speed of the qubit readout. In this dissertation we study some aspects of the dispersive readout of superconducting qubits, and introduce tools and methods for studying these systems.In Chapter 2 we show that in presence of neighboring qubits, the system is typically measured in the basis of joint eigenstates of qubits, in contrast to what is expected from the textbook collapse postulate. In such setups, the excitation can switch between the eigenstates, leading to measurement error. In Chapter 3 we study the joint state of the qubit-resonator system during the measurement, and show that the qubit-induced nonlinearity of the resonator squeezes its state, and within the rotating wave approximation (RWA) the system mostly remains in the joint eigenladder that is associated with the qubit's initial state. In Chapter 4 we show that built-in energy resonances in the qubit-resonator Jaynes-Cummings ladder occur at specific resonator populations, and the couplings between these resonant levels are provided by the usually neglected non-RWA terms. Such resonances lead to measurement deterioration by exciting the qubit out of the computational subspace. In Chapter 5 we provide a hybrid phase-space-Fock-space approach for studying the evolution and squeezing of driven nonlinear resonators within Gaussian approximation, which is numerically efficient and sufficiently accurate. In Chapter 6 we study the propagating squeezed field that leaks out of the resonator, and write evolution equations for the correlators of the measured field quadrature. These equations are easy to simulate and can describe the squeezing of the propagating field during the transient, which can be used to optimize the fidelity and speed of the quadrature measurement in the dispersive readout of superconducting qubits.