In this manuscript, we examine design strategies for the development of excitonic circuits that are capable of performing simple 2-qubit multi-step quantum algorithms. Specifically, we compare two different strategies for designing dye-based systems that prescribe exciton evolution encoding a particular quantum algorithm. A serial strategy implements the computation as a step-by-step series of circuits, with each carrying out a single operation of the quantum algorithm, and a combined strategy implements the entire computation in a single circuit. We apply these two approaches to the well-studied Deutsch–Jozsa algorithm and evaluate circuit fidelity in an idealized system under a model harmonic bath, and also for a bath that is parameterized to reflect the thermal fluctuations of an explicit molecular environment. We find that the combined strategy tends to yield higher fidelity and that the harmonic bath approximation leads to lower fidelity than a model molecular bath. These results imply that the programming of excitonic circuits for quantum computation should favor hard-coded modules that incorporate multiple algorithmic steps and should represent the molecular nature of the circuit environment.