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Quantum circuit model
Computation desk
A quantum circuit is an ordered list of reversible operations on qubits, then a measurement. The computation desk uses that split to write a problem down before any simulator or device is chosen.
Qubits as the working unit
A qubit is a two-level system. Its pure state is a normalised complex vector in two dimensions. The labels |0⟩ and |1⟩ are the outcomes a later measurement can return. A single-qubit state is a weighted sum of those labels. The weights are amplitudes.
A classical bit is already 0 or 1. A qubit is not secretly one of those values before readout. Measurement returns one label and drops the rest of the superposition. That is why the desk writes the unitary evolution first and the readout second, in the note on measurement and sampling.
Gates are reversible linear maps
A gate is a unitary matrix: it keeps vector length and can be undone by its conjugate transpose. Hadamard builds an equal superposition from |0⟩. The Pauli maps flip a basis state or a relative phase. A controlled-NOT ties two qubits so the target flips only when the control is |1⟩. Rotations such as R_z(θ) carry the angles a later optimiser may change.
Composition of gates is matrix multiplication, yet the desk does not store the full matrix. It stores which qubits, which angle, and which time step. That list can be replayed by state-vector simulation or passed into hybrid execution.
Width, depth, and entanglement
Width is how many qubits the circuit touches. Depth is how many time steps remain after gates on disjoint qubits are allowed to run together. Width sets the memory of an exact state. Depth sets runtime and, on a device, how long the state is exposed to noise.
Entanglement is correlation that cannot be written as a product of single-qubit states. It appears when a superposition on one qubit is copied into a correlation with another. Product states stay small to store. Entangled states do not. That fork is why the next notes separate state-vector simulation from tensor-network contraction.
A product state of n qubits can be stored with a few amplitudes per qubit. A general pure state needs one amplitude for every basis string, which doubles with each added qubit. Depth does not change that count. It changes the cost of updating it, and how much noise and error a device accumulates.
Finding from this desk
The desk’s working finding is that a research claim should travel as a gate list, not as a vendor-specific program. The list names qubits, gates, and the moment each gate runs. Readout is a second step.