Quantum computing literature is unstandardized and often-times unwieldy. We design and formalise explicit quantum algorithms with rubrics, pseudocode, quantum circuit diagrams, and exact order-of-magnitude expressions for their complexity. We devise new linear quantum algorithms for representing permutations of objects that outperform the previous world standard. Nonlinear quantum computing is a speculative field, and has the potential to solve NP-complete and harder problems. We find shortcomings in existing nonlinear quantum algorithms, and devise our own explicit algorithm that leaves no doubt as to the power of nonlinear quantum computing. Our work shows the advantage of making quantum algorithms explicit.