The gate boxes in this lesson are promises about the intended state map, not pictures of the actual machine. Preparation, gates, and readout are drawn as clean boxes so the logic ledger is easy to audit before adding control pulses and readout hardware. Real devices add isolation, calibration, drift, decoherence, detector noise, finite shots, and uncertainty around the same ideal contract.

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\text{ideal box} \ne \text{full hardware model}
Ideal gate boxThe gate box is a checked state map, not device physics.state1 zero0 onestate1/sqrt(2) zero1/sqrt(2) oneHgate

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\text{hardware constants are deferred}
Ideal gate boxThe exact claim is only the finite state map.state1 zero0 onestate1/sqrt(2) zero1/sqrt(2) oneHgate

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.

state map→hardware budget later\text{state map} \rightarrow \text{hardware budget later}
Ideal gate boxThe first quantum book keeps only the finite map.state1 zero0 onestate1/sqrt(2) zero1/sqrt(2) oneHgate