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arXiv:1109.5562 · Physical Review B

Qubit state detection using the quantum Duffing oscillator

Vicente Leyton‐Ortega, Michael Thorwart, Vittorio Peano

Published Oct 3, 2011• 7 citations
arXivHTMLPDF

Abstract

We introduce a detection scheme for the state of a qubit that is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the qubit and is used as its detector. Close to the fundamental resonator frequency, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the qubit state, these few-photon resonances are shifted to different driving frequencies. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced readout fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current qubit inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.

DOI
10.1103/physrevb.84.134501

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We introduce a detection scheme for the state of a qubit that is based on resonant few-photon transitions in a driven nonlinear resonator. The latter is parametrically coupled to the qubit and is used as its detector. Close to the fundamental resonator frequency, the nonlinear resonator shows sharp resonant few-photon transitions. Depending on the qubit state, these few-photon resonances are shifted to different driving frequencies. We show that this detection scheme offers the advantage of small back action, a large discrimination power with an enhanced readout fidelity, and a sufficiently large measurement efficiency. A realization of this scheme in the form of a persistent current qubit inductively coupled to a driven SQUID detector in its nonlinear regime is discussed.
We propose a threshold detector with an operating principle based on a parametric period-doubling bifurcation in an externally pumped nonlinear resonance circuit. The ac-driven resonance circuit includes a dc-current--biased Josephson junction ensuring parametric frequency conversion (period-doubling bifurcation) due to its quadratic nonlinearity. A sharp onset of oscillations at the half-frequency of the drive allows for the detection of small variations of an effective inductance and, therefore, the readout of the quantum state of a coupled Josephson qubit. The bifurcation characteristics of this circuit are compared with those of the conventional Josephson bifurcation amplifier, and its possible advantages are discussed.
Abstract—We have implemented a resonant circuit that uses a SQUID as a flux-sensitive Josephson inductor for qubit readout. In contrast to the conventional switching current measurement that generates undesired quasiparticles when the SQUID switches to the voltage state, our approach keeps the readout SQUID biased along the supercurrent branch during the measurement. By in-corporating the SQUID inductor in a high-Q resonant circuit, we can distinguish the two flux states of a niobium persistent-current (PC) qubit by observing a shift in the resonant frequency of both the magnitude and the phase spectra. The readout circuit was also characterized in the nonlinear regime to investigate its potential use as a nonlinear amplifier. Index Terms—Nonlinear oscillators, persistent-current qubits, resonant circuits, SQUIDs. I.
We determine the optimal parameters for a simple and efficient scheme of dispersive readout of a qubit. Depending on the qubit state (ground or excited), the resonance of a cavity is shifted either to the red or to the blue side. Qubit state is inferred by detecting the photon number transmitted through the cavity. It turns out that this kind of detection provides better measurement fidelity than the detection of the presence or absence of photons only. We show that radiating the cavity on either of the frequencies it shifts to results in a suboptimal measurement. The optimal frequency of the probe photons is determined, as well as the optimal ratio of the shift to the resonator leakage. It is shown that to maximize the fidelity of a long-lasting measurement, it is sufficient to use the parameters optimizing the signal-to-noise ratio in the photon count. One can reach 99% fidelity for a single-shot measurement in various physical realizations of the scheme.
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.
We have implemented a resonant circuit that uses a SQUID as a flux-sensitive Josephson inductor for qubit readout. In contrast to the conventional switching current measurement that generates undesired quasiparticles when the SQUID switches to the voltage state, our approach keeps the readout SQUID biased along the supercurrent branch during the measurement. By incorporating the SQUID inductor in a high-Q resonant circuit, we can distinguish the two flux states of a niobium persistent-current (PC) qubit by observing a shift in the resonant frequency of both the magnitude and the phase spectra. The readout circuit was also characterized in the nonlinear regime to investigate its potential use as a nonlinear amplifier.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.