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Journal of Physics Conference Series

Superconducting non-linear resonator for non-destructive readout of a flux qubit

K. Inomata, 道生 渡部, Tsuyoshi Yamamoto, Kazuaki Matsuba, Yasunobu Nakamura, J. S. Tsai

Published Mar 1, 2009• 4 citations
Publisher

Abstract

We have investigated microwave response of a λ/4 superconducting coplanar waveguide resonator which is terminated by a DC-SQUID coupled with a flux qubit. The circuit is designed for non-destructive single-shot readout of a flux qubit based on dispersive interaction between the qubit and the resonator and switching between bistable states of the driven nonlinear resonator. A high-frequency (∼ 10 GHz) resonator is exploited for suppressing photon-number fluctuations which cause qubit dephasing even when the readout circuit is not activated. We observed bifurcation of the resonator in the nonlinear driving regime. In the linear regime, the degeneracy point of the qubit was detected as a shift of the resonant frequency.

DOI
10.1088/1742-6596/150/5/052077

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We have investigated microwave response of a λ/4 superconducting coplanar waveguide resonator which is terminated by a DC-SQUID coupled with a flux qubit. The circuit is designed for non-destructive single-shot readout of a flux qubit based on dispersive interaction between the qubit and the resonator and switching between bistable states of the driven nonlinear resonator. A high-frequency (∼ 10 GHz) resonator is exploited for suppressing photon-number fluctuations which cause qubit dephasing even when the readout circuit is not activated. We observed bifurcation of the resonator in the nonlinear driving regime. In the linear regime, the degeneracy point of the qubit was detected as a shift of the resonant frequency.
We control the transition frequency of a superconducting flux qubit coupled to a frequency-tunable resonator comprising a direct current superconducting quantum interference device (dc SQUID) by microwave driving. The dc SQUID mediates the coupling between microwave photons in the resonator and a flux qubit. The polarity of the frequency shift depends on the sign of the flux bias for the qubit and can be both positive and negative. The absolute value of the frequency shift becomes larger by increasing the photon number in the resonator. These behaviors are reproduced by a model considering the magnetic interaction between the flux qubit and dc SQUID. The tuning range of the transition frequency of the flux qubit reaches $\ensuremath{\approx}1.9\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$. The effect of photon number fluctuation in the resonator to the dephasing rate of the flux qubit is also discussed.
Recently the exploration of nonlinear microwave response in superconducting circuits has been extended to Nb nanobridges that can operate at higher magnetic fields, frequencies, and temperatures than their conventional Al counterparts. Nb nanobridge-based Superconducting Quantum Interference Devices (SQUIDs) have shown potential applications in quantum information processing, weak signal detection, and single spin detection. Combining such non-linear elements with circuit Quantum Electrodynamic (QED) elements like coplanar waveguide (CPW) resonators allows the study of the nonlinearity of such systems. In this work we report on the design, fabrication and dispersive microwave readout of a Nb DC nanoSQUID embedded in a superconducting quarter-wavelength resonator. The measured flux-tuneability of the resonance shows a modulation of a few MHz and fits simulations, giving a critical current of 330 μA and a screening parameterβLof 4.07. Following this we present results showing Kerr-type detuning with a pump tone applied to the device.
We present experimental results on a dispersive scheme for reading out a Josephson phase qubit. A capacitively shunted dc-SQUID is used as a nonlinear resonator which is inductively coupled to the qubit. We detect the flux state of the qubit by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, we reduce the qubit state measurement time down to 25 microseconds, which is much faster than using the conventional readout performed by switching the SQUID to its non-zero dc voltage state. The demonstrated readout scheme allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.
Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.
A nonlinear resonant circuit comprising a SQUID magnetometer and a shunting capacitor is studied as a readout scheme for a persistent-current qubit. The flux state of the qubit is detected as a change in the Josephson inductance of the SQUID magnetometer, which in turn mediates a shift in the resonant frequency of the readout circuit. The nonlinearity and resulting hysteresis in the resonant behavior are characterized as a function of the power of both the input drive and the associated resonance-peak response. Numerical simulations based on a nonlinear circuit model shows that the observed nonlinearity is dominated by the effect due to an ac flux rather than current bias through the Josephson inductor.
We demonstrate high-contrast state detection of a superconducting flux qubit. Detection is realized by probing the microwave transmission of a nonlinear resonator, based on a SQUID. Depending on the driving strength of the resonator, the detector can be operated in the monostable or the bistable mode. The bistable operation combines high-sensitivity with intrinsic latching. The measured contrast of Rabi oscillations is as high as 87%; of the missing 13%, only 3% of the loss of contrast is unaccounted for. Experiments involving two consecutive detection pulses are consistent with preparation of the qubit state by the first measurement.