  We present a scheme for linear optical quantum computing using time-bin
encoded qubits in a single spatial mode. We show methods for single-qubit
operations and heralded controlled phase (CPhase) gates, providing a sufficient
set of operations for universal quantum computing with the
Knill-Laflamme-Milburn scheme. Our scheme is suited to available photonic
devices and ideally allows arbitrary numbers of qubits to be encoded in the
same spatial mode, demonstrating the potential for time-frequency modes to
dramatically increase the quantum information capacity of fixed spatial
resources. As a test of our scheme, we demonstrate the first entirely single
spatial mode implementation of a two-qubit quantum gate and show its operation
with an average fidelity of 0.84+-0.07.
