Key papers
The published work worth reading, grouped by what you are trying to do. Each entry says why it matters rather than just restating the abstract — a reading list is only useful if it tells you what to skip. Every link goes to arXiv, so all of it is free.
Read these three, in order
Preskill's NISQ era paper for calibration, Cerezo's Variational Quantum Algorithms review for the landscape, then McClean's barren plateaus for the constraint that shapes everything else. That is a weekend, and it will save you from a lot of over-optimistic reading later.
Always find the classical baseline
The tensor-network papers here are not a detour — they are the competition. Most claimed quantum advantages evaporate when someone runs a well-tuned classical method on the same problem. Before believing any speedup, including your own, go and look for what DMRG does with it.