High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Jaynes-Cummings Nonlinearity

Abstract

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that in the strongly-driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.Circuit quantum electrodynamics (cQED) is the study of the interaction of light and matter where superconducting qubits playing the role of atoms are strongly coupled to microwave transmission line resonators acting as cavities [1]. This architecture offers advantages over cavity QED with atomic systems with regard to both coupling strength and accessibility of strongly driven nonlinear regimes [2][3][4]. For example, the high-power response of a cavity with a qubit in resonance has recently been studied, demonstrating the appearance of additional photon number (n) resonances with characteristic √ n spacing, in excellent agreement with theory [4]. In this Letter, we investigate the behavior of a strongly driven cQED system in the dispersive regime, where four strongly coupled transmon qubits [5] are far detuned from the cavity. We find that for increasing drive strength, the cavity response initially becomes strongly nonlinear and continuously shifts down in frequency. At a critical power, it reaches its bare frequency and transmission rapidly rises to a "bright state". Importantly, this critical power is strongly dependent on the initial state of the qubit, providing for a simple high-fidelity qubit readout mechanism. This scheme is also applicable to the joint measurement of several qubits simultaneously.There are two commonly used cQED readout schemes. The first employs the state-dependent dispersive shift of the coupled cavity's resonance frequency [ Fig. 1(a)] to infer the qubit state by measuring transmission [6,7]. This must be done in the low-power, linear response regime of the cavity in part because system anharmonicity inhibits higher population. The signal-to-noise ratio (SNR) and fidelity of this weak measurement is thus limited (to typically 40%-60% [7,8]) by the relatively high noise temperature (T sys N ≈ 10 K ∼ 20 photons) of conventional commercial amplifiers and short integration time mandated by qubit relaxation (T 1 ≈ 1 µs) [9]. A specialized superconducting low-noise amplifier [10][11][12] could improve the SNR, but at a cost of additional complexity. The second scheme uses some nonlinearity to project the qubit state onto a classically distinguishable system and yield high discrimination [13]. The Josephson bifurcation amplifier (JBA) is one such example, exploiting cavity bistability caused by the Kerr-Duffing nonlinearity of an additional Josephson junction [14][15][16]. These schemes have, however, not yet taken advant...

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