It is a widely held belief that a computational architecture based on quantum systems will bring forth major technological advances in a plethora of fields whose names significantly overlap with information technology buzzwords. While it is true that there are some problems where quantum algorithms could offer significant advantage, these problems are somewhat narrow, and to make generalist claims of quantum speedup in machine learning, artificial intelligence and pattern recognition we should read the fine print of actual requirements to load information into quantum systems (S. Aaronson, 2015). However, what if the quantum advantage were built into the loading itself? Is that even possible, in terms of information? Most quantum algorithms employ amplitude encodings or basis encodings to load classical information into quantum systems. However, a straightforward approach to encode information that must later be retrieved is an observable encoding, where classical data is associated to the outcome of observables measured over a quantum state. One of the novel aspects of this type of encoding is the natural extension to multiple measurement bases and introducing measurement-basis choice as part of a quantum algorithm. In the literature, similar encodings have been explored for quantum generative models of quantum statistics with Boltzmann and Born machines, but the most explicit scheme based on an observable encoding is a Quantum Random Access Code (QRAC), where choosing an observable to measure allows to retrieve a fragment of the encoded information with some success probability. QRACs have been shown to showcase advantage over their classical counterpart, but have only been studied in depth up to n = 3 qubits, due to the mathematical complexity of constructing a class of many-qubit observables organized into unbiased bases.

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