  General purpose quantum computers can, in principle, entangle a number of
noisy physical qubits to realise composite qubits protected against errors.
Architectures for measurement-based quantum computing intrinsically support
error-protected qubits and are the most viable approach for constructing an
all-photonic quantum computer. Here we propose and demonstrate an integrated
silicon photonic architecture that both entangles multiple photons, and encodes
multiple physical qubits on individual photons, to produce error-protected
qubits. We realise reconfigurable graph states to compare several schemes with
and without error-correction encodings and implement a range of quantum
information processing tasks. We observe a success rate increase from 62.5% to
95.8% when running a phase estimation algorithm without and with error
protection, respectively. Finally, we realise hypergraph states, which are a
generalised class of resource states that offer protection against correlated
errors. Our results show how quantum error-correction encodings can be
implemented with resource-efficient photonic architectures to improve the
performance of quantum algorithms.
