We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories.

Initialization and read-out of coupled quantum systems are essential ingredients for the implementation of quantum algorithms1, 2. Single-shot read-out of the state of a multi-quantum-bit (multi-qubit) register would allow direct investigation of quantum correlations (entanglement), and would give access to further key resources such as quantum error correction and deterministic quantum teleportation1. Although spins in solids are attractive candidates for scalable quantum information processing, their single-shot detection has been achieved only for isolated qubits3, 4, 5, 6.