Quantum repeater systems and apparatus for quantum communication. In one aspect, a system includes a quantum signal receiver configured to receive a quantum field signal; a quantum signal converter configured to: sample quantum analog signals from a quantum field signal received by the quantum signal receiver; encode sampled quantum analog signals as corresponding digital quantum information in one or more qudits, comprising applying a hybrid analog-digital encoding operation to each quantum analog signal and a qudit in an initial state; decode digital quantum information stored in the one or more qudits as a recovered quantum field signal, comprising applying a hybrid digital-analog decoding operation to each qudit and a quantum analog register in an initial state; a quantum memory comprising qudits and configured to store digital quantum information encoded by the quantum signal converter; and a quantum signal transmitter configured to transmit the recovered quantum field signal.