We present a method for measuring the internal state of a superconducting qubit inside an on-chip microwave resonator. We show that one qubit state can be associated with the generation of an increasingly large cavity coherent field, while the other remains associated with the vacuum. By measuring the outgoing resonator field with conventional devices, an efficient single-shot QND-like qubit readout can be achieved, enabling a high-fidelity measurement in the spirit of the electronshelving technique for trapped ions. We expect that the proposed ideas can be adapted to different superconducting qubit designs and contribute to the further improvement of qubit readout fidelity.PACS numbers: 03.65. Yz, 03.67.Lx, 03.65.Wj, 42.50.Lc Superconducting nanocircuits [1,2] are considered promising candidates for diverse implementations of quantum information tasks [3]. In this context, circuit quantum electrodynamics (QED) [4,5], which studies superconducting qubits [1,6] coupled to on-chip microwave resonators, occupies a central role. To achieve the desired goals, it is important to implement high-fidelity two-qubit gates [7] and efficient schemes to read out the qubit state [8]. In both cases, trapped-ion systems represent the state-of-the-art for qubit realizations [9]. In particular, electron-shelving qubit readout has produced fidelity benchmarks of approximately 99.99% [10]. These astonishing achievements suggest the potential impact of transferring key ideas from quantum optics to circuit QED. Unfortunately, electron shelving relies strongly on the use of single-photon detectors [9], which are unavailable in microwave technology in the range 1−10 GHz [11]. Nevertheless, in this manuscript we show that a singleshot QND-like fast qubit readout can be designed by exploiting the electron-shelving concept in circuit QED.We first present the physics of electron shelving in trapped ions. In Fig. 1, we show a three-level atom where an unknown qubit state |ψ = α|g + β|e is encoded in states |g and |e . Via a laser beam, the ground state |g is coupled to a third level |u , which can decay producing a continuous cyclic transition. In this case, the qubit is projected onto state |g and many photons are emitted in free space, one at each cycle. In contrast, when the qubit is projected onto state |e , no photons are emitted. A lens is used to collect the photons more efficiently by improving the solid angle. Although the photodetector has a low efficiency η d , the qubit readout fidelity can be very high. Typically, it is estimated through F = 1 − e −η d N , which rapidly approaches unity for η d N ≫ 1, N being the number of detected photons. Key elements for electron cyclic transition Photodetector lens FIG. 1: (Color online) Sketch of electron shelving in trapped ions. The |g ↔ |u transition is driven with a laser beam, performing a cyclic transition and emitting many photons when |g is projected. No photons are detected when |e is measured. Undesired transitions are inhibited via selection rules.shelving are the use of three...
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