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Qusp is an abbreviation for Quantum Singleton Processor.

The processor itself is not necessarily tied to Singleton Universe posthumans - it could conceivably be used for non-sapient algorithms, as well. It's considered by several characters in Egan's works to be a pivotal invention paving the way to 'civilisation', owing to the attributes that give it its name:

By isolating decision making from the outside world on a quantum level, bearers of Qusps only ever make one choice, rather than leaving copies of themselves in the future quantum multiverse (of that decision in particular) to make others. That way, for every choice a Qusp posthuman makes, they do not doom versions of themselves to making worse choices - but they also can't take comfort that a different version of themselves might have made a better choice, in turn. In consequence, decisions matter to Qusp posthumans far more even than for their human ancestors.

Cass dated the advent of civilisation to the invention of the quantum singleton processor. The Qusp. She accepted the fact that she couldn’t entirely avoid splitting into multiple versions; interacting with any ordinary object around her gave rise to an entangled system — Cass plus cloud, Cass plus flower — and she could never hope to prevent the parts that lay outside her from entering superpositions of different classical outcomes, generating versions of her who witnessed different external events.
Unlike her hapless ancestors, though, she did not contribute to the process herself. While the Qusp inside her skull performed its computations, it was isolated from the wider world — a condition lasting just microseconds at a time, but rigidly enforced for the duration — only breaking quarantine when its state vector described one outcome, with certainty. With each operating cycle, the Qusp rotated a vector describing a single alternative into another with the same property, and though the path between the two necessarily included superpositions of many alternatives, only the final, definite state determined her actions.
Being a singleton meant that her decisions counted. She was not forced to give birth to a multitude of selves, each responding in a different way, every time she found her conscience or her judgement balanced on a knife-edge. She was not at all what Homo sapiens had actually been, but she was close to what they’d believed themselves to be, for most of their history: a creature of choice, capable of doing one thing and not another.
- taken from Schild's Ladder

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