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State-vector simulation
Simulation desk
State-vector simulation applies each gate to the full list of amplitudes. The simulation desk uses it as the exact reference for small circuits from the quantum circuit model.
What is stored
The state of n qubits is an array of 2^n complex amplitudes, one for each bit string. Applying a single-qubit gate touches pairs of entries. A two-qubit gate touches groups of four. The array is the entire description of a pure state.
The quantum circuit model supplies the gate list. The simulator never invents extra qubits and never skips a controlled operation. If the list says the gate acts on qubits 0 and 3, those indices are the only ones updated.
Where the method stops
Memory grows as 2^n. Around thirty qubits the array is already about a billion complex numbers. The desk treats that wall as a fact of the method, not as a bug in the code. Beyond it, the same circuit is handed to tensor-network contraction when the entanglement stays limited.
A matching run on a handful of qubits is still required. The desk compares a sample of exact amplitudes, or of Born probabilities, with the compressed method before any larger claim is written down. Readout itself is described under measurement and sampling.
Finding from this desk
Exact simulation is the desk’s reference instrument. It is trustworthy while the state still fits in memory, and it is the check every compressed method has to match on a small circuit.