We investigate the effective interaction between two microwave fields, mediated by a transmon-type superconducting artificial atom which is strongly coupled to a coplanar transmission line. The interaction between the fields and atom produces an effective cross-Kerr coupling. We demonstrate average cross-Kerr phase shifts of up to 20 degrees per photon with both coherent microwave fields at the single-photon level. Our results provide an important step toward quantum applications with propagating microwave photons.

The ability to nondestructively detect the presence of a single, traveling photon has been a long-standing goal in optics, with applications in quantum information and measurement. Realizing such a detector is complicated by the fact that photon-photon interactions are typically very weak. At microwave frequencies, very strong effective photon-photon interactions in a waveguide have recently been demonstrated. Here we show how this type of interaction can be used to realize a quantum nondemolition measurement of a single propagating microwave photon. The scheme we propose uses a chain of solid-state three-level systems (transmons) cascaded through circulators which suppress photon backscattering. Our theoretical analysis shows that microwave-photon detection with fidelity around 90% can be realized with existing technologies. DOI: 10.1103/PhysRevLett.112.093601 PACS numbers: 42.50.Dv, 42.50.Lc, 42.65.-k, 85.60.Gz Quantum mechanics tells us that a measurement perturbs the state of a quantum system. In the most extreme case, this leads to the destruction of the measured quantum system. By coupling the system to a quantum probe, a quantum nondemolition [1] (QND) measurement can be realized, where the system is not destroyed by the measurement. Such a property is crucial for quantum error correction [2], state preparation by measurement [3,4], and one-way quantum computing [5]. For microwave frequencies, detection of confined photons in high-Q cavities has been proposed and experimentally demonstrated by several groups [6][7][8][9]. They all exploit the strong interaction between photons and atoms (real and artificial) on the single photon level. Detection schemes for traveling photons have also been suggested [10][11][12], but in those proposals the photon is absorbed by the detector and the measurement is therefore destructive. Proposals for detecting itinerant photons using coupled cavities have also been suggested, but they are limited by the trade-off between interaction strength and signal loss due to reflection [13]. Other schemes based on the interaction of Λ-type atomic level structures have been suggested, but the absence of such atomic level structures in solid-state systems make them unsuited to the microwave regime [14][15][16].Here, we present a scheme to detect a propagating microwave photon in an open waveguide. At its heart is the strong effective nonlinear interaction between microwave fields induced by an artificial atom to which they are coupled. A single photon in the control field induces a detectable displacement in the state of a probe field, which is initially in a coherent state. The control field is not absorbed, making the protocol QND. The protocol may be operated either synchronously (in which the control photons arrive within specified temporal windows) or asynchronously [17]. Figure 1 illustrates the scheme. The effective nonlinear interaction between the control photon and the probe field is realized by N noninteracting artificial atoms (transmon devices [18]) coupled to the tran...

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Deep Neural Networks (DNN) have improved the quality of several non-safety related products in the past years. However, before DNNs should be deployed to safety-critical applications, their robustness needs to be systematically analyzed. A common challenge for DNNs occurs when input is dissimilar to the training set, which might lead to high confidence predictions despite proper knowledge of the input.Several previous studies have proposed to complement DNNs with a supervisor that detects when inputs are outside the scope of the network. Most of these supervisors, however, are developed and tested for a selected scenario using a specific performance metric. In this work, we emphasize the need to assess and compare the performance of supervisors in a structured way. We present a framework constituted by four datasets organized in six test cases combined with seven evaluation metrics.The test cases provide varying complexity and include data from publicly available sources as well as a novel dataset consisting of images from simulated driving scenarios. The latter we plan to make publicly available. Our framework can be used to support DNN supervisor evaluation, which in turn could be used to motive development, validation, and deployment of DNNs in safety-critical applications.