Abstract:Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here, we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasiparticle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup we perform single-shot readout of this "Andreev qubit". We determine its excited state lifetime and coherence time to be in the microsecond range.Quantum jumps and parity switchings are observed in continuous measurements. In addition to possible quantum information applications, such Andreev qubits are a testbed for the physics of single elementary excitations in superconductors. 2The ground state of a uniform superconductor is a many-body coherent state. Microscopic excitations of this superconducting condensate, which can be created for example by the absorption of photons of high enough energy, are delocalized and incoherent because they have energies in a continuum of states. Localized states arise in situations where the superconducting gap Δ or the superconducting phase undergo strong spatial variations: examples include Shiba states around magnetic impurities (1), Andreev states in vortices (2) or in weak links between two superconductors (3). Because they have discrete energies within the gap, Andreev states are expected to be amenable to coherent manipulation (4,5,6,7,8). In the simplest weak link, a single conduction channel shorter than the superconducting coherence length  , there are only two Andreev levels, governed by the transmission probability  of electrons through the channel and the phase difference  between the two superconducting condensates (3). Despite the absence of actual barriers, quasiparticles (bogoliubons) occupying these Andreev levels are localized over a distance  around the weak link by the gradient of the superconducting phase, and the system can be considered an "Andreev quantum dot " (5,6). Figure 1 EE (13,14). The e state can also be reached directly from g by absorption of a photon of energy 2.A EHere we demonstrate experimentally the manipulation of coherent superpositions of states g and , e even if parasitic transitions to o are also observed.3 Atomic-size contacts are suitable systems to address the Andreev physics because they accommodate a small number of short conduction channels (15). We create them using the microfabricated break-junction technique (16). (Fig. 3D). The analysis (23) of this real-time trace yields a parity switching rate of 50kHz (20). 5The coherent manipulation at   of the two-level system formed by g and e is illustrated in Fig. 4. Figure 4A shows the Rabi oscillations between g and e obtained by varying the duration of a driving pulse at frequency 1 ( , )A ff   (Movie S1). Figure 4B shows how the populations of g and e change when the driving pulse frequency ...