The paper, posted to the arXiv preprint server and written in part by researchers affiliated with the Open Quantum Institute hosted at CERN, is a synthesis of existing research. It covers number theory, optimization, statistical inference, quantum simulation, linear algebra and the analysis of structure in data, with potential applications in chemistry, materials, signal processing and code breaking. The evidence and maturity vary widely across entries.
The researchers focus on speedups greater than quadratic, which they argue will likely be needed to overcome the high operating costs of early error-corrected quantum computers. A quadratic speedup means, for example, a thousand steps instead of a million, but not necessarily finishing a thousand times faster, because each quantum step costs more.
According to The Quantum Insider, the paper cautions that a theoretical advantage does not guarantee faster results in practice: preparing data, correcting errors and reading results can erase the savings. Comparisons are against the best classical methods known today, which may improve, and the researchers recommend starting with tasks where quantum advantage is already well supported.