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The ability to tailor the hopping interactions between the constituent elements of a physical system could enable the observation of unusual phenomena that are otherwise inaccessible in standard settings1,2. In this regard, a number of recent theoretical studies have indicated that an asymmetry in either the short- or long-range complex exchange constants can lead to counterintuitive effects, for example, the possibility of a Kramer’s degeneracy, even in the absence of spin 1/2 or the breakdown of the bulk–boundary correspondence3–8. Here we show how such tailored asymmetric interactions can be realized in photonic integrated platforms by exploiting non-Hermitian concepts, enabling a class of topological behaviours induced by optical gain. As a demonstration, we implement the Haldane model, a canonical lattice that relies on asymmetric long-range hopping to exhibit quantum Hall behaviour without a net external magnetic flux. The topological response observed in this lattice is a result of gain and vanishes in a passive but otherwise identical structure. Our findings not only enable the realization of a wide class of non-trivial phenomena associated with tailored interactions, but also open up avenues to study the role of gain and nonlinearity in topological systems in the presence of quantum noise. Non-Hermitian concepts together with optical gain allow the tailoring of short- and long-range exchange interactions in integrated topological photonics, and an exact Haldane model can be realized in this way.