The finite-state diagrams are idealized prepare, gate, and measure boxes, not a full hardware model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The gate box is an idealized physical operation
The diagram treats preparation, gates, and readout as ideal boxes. Real devices need isolation, control, calibration, and readout hardware.
ideal box=full hardware model
Real hardware numbers are deferred
This first quantum book does not use coherence times, gate fidelities, control pulses, or error-correction thresholds as numeric claims.
hardware constants are deferred
The ideal map is a contract for later hardware books
The box says what state map is intended. Later hardware books add pulses, calibration, readout noise, and error budgets around that same contract.