In this paper, the design of multi-hop physical layer network coding (PNC) is investigated. In the existing multi-hop PNC designs, the effects of error propagation and mutual-interference are not well addressed. Error propagation refers to that the estimation error at any node may propagate to the neighboring nodes, which may result in serious end-to-end bit errors. The impact of the mutual-interference from other transmitting nodes to a receiver determines the upper bound SINR of two neighboring nodes given end-to-end SNR. By carefully addressing these issues, we propose two multi-hop PNC designs, the direct multi-hop PNC (D-MPNC) and the stored multi-hop PNC (S-MPNC), where both designs achieve the throughput upper bound of one symbol per symbol duration, which is the same as that of the traditional PNC with a single relay. There is a tradeoff between the applications of D-MPNC and S-MPNC, which targets for simple-implementation and optimal end-to-end bit error rate (BER), respectively. We provide the detailed designs of D-MPNC and S-MPNC and obtain the end-to-end BER bounds theoretically. Extensive simulation results demonstrate the performance gain of the proposed multi-hop PNC compared with the traditional PNC in terms of end-to-end BER and end-to-end throughout.