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The propagation of N photons in one dimensional waveguides coupled to M qubits is discussed, both in the strong and ultrastrong qubit–waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear limit for the scattered photons as a function of N, M, qubit inter distance and light–matter coupling. The quantum evolution is numerically solved via the matrix product states technique. The time evolutions for both the field and qubits are computed.doi:10.1039/c4fd00206g pmid:25760380 fatcat:jdjjugihjfh4ppifxxlubq7apq