Future multi-photon applications of quantum optics and quantum information science require quantum memories that simultaneously store many photon states, each encoded into a different optical mode, and enable one to select the mapping between any input and a specific retrieved mode during storage. Here we show, with the example of a quantum repeater, how to employ spectrallymultiplexed states and memories with fixed storage times that allow such mapping between spectral modes. Furthermore, using a Ti:Tm:LiNbO3 waveguide cooled to 3 Kelvin, a phase modulator, and a spectral filter, we demonstrate storage followed by the required feed-forward-controlled frequency manipulation with time-bin qubits encoded into up to 26 multiplexed spectral modes and 97% fidelity.PACS numbers: 03.67. Hk, 42.50.Ex, 32.80.Qk, 78.47.jf Further advances towards scalable quantum optics [1,2] and quantum information processing [3,4] rely on joint measurements of multiple photons that encode quantum states (e.g. qubits) [3][4][5]. However, as photons generally arrive in a probabilistic fashion, either due to a probabilistic creation process or due to loss during transmission, such measurements are inherently inefficient. For instance, this leads to exponential scaling of the time required to establish entanglement, the very resource of quantum information processing, as a function of distance in a quantum relay [6]. This problem can be overcome by using quantum memories, which are generally realized through the reversible mapping of quantum states between light and matter [7,8]. For efficient operation, these memories must be able to simultaneously store many photon states, each encoded into a different optical mode, and subsequently (using feed-forward) allow selecting the mapping between input and retrieved modes (e.g., different spectral or temporal modes). This enables making several photons arriving at a measurement device indistinguishable, thereby rendering joint measurements deterministic. For instance, revisiting the example of entanglement distribution, a quantum relay supplemented with quantum memories changes it to a repeater and, in principle, the scaling from exponential to polynomial [4,9].Interestingly, for such multimode quantum memories to be useful, it is not necessary to map any input mode onto any retrieved (output) mode, but it often suffices if a single input mode, chosen once a photon is stored, can be mapped onto a specific output mode (e.g. characterized by the photon's spectrum and recall time) [4,10]. This ensures that the photons partaking in a joint measurement, each recalled from a different quantum memory, are indistinguishable, as required, e.g., for a Bell-state measurement. We emphasize that it does not matter if the device used to store quantum states also allows the mode mapping, or if the mode mapping is performed after recall using appended devices -we will refer to the system allowing storage and mode mapping as the memory.To date, most research assumes photons arriving at different times at the m...