The Quantum Circuit Model
The circuit model describes computation as qubits initialised, transformed by a sequence of gates, then measured to produce classical output.
The dominant framework
The quantum circuit model is the standard way to express quantum algorithms, analogous to Boolean circuits for classical computing. A computation is a register of qubits, a time-ordered sequence of gates, and a final measurement.
The three stages
- Initialise: prepare all qubits in a known state, usually |000...0>
- Evolve: apply a sequence of unitary gates from a universal set
- Measure: read out qubits, producing classical bits as the result
Reading a circuit diagram
In a diagram, each horizontal wire is a qubit and time flows left to right. Boxes on wires are single-qubit gates; a vertical line joining a filled dot to a target symbol is a controlled gate like CNOT. Meters denote measurements. The whole diagram is one large unitary followed by measurement.
Depth and width
Two resource measures dominate. Width is the number of qubits; depth is the number of sequential gate layers. Because decoherence limits how long qubits stay coherent, shallow circuits are strongly preferred on near-term hardware. Optimising a circuit usually means reducing depth and two-qubit gate count.
Relation to other models
The circuit model is equivalent in power to measurement-based, adiabatic, and topological quantum computing — each can simulate the others with polynomial overhead. The circuit model is the default because it maps directly onto gate-based hardware and makes algorithm analysis, resource counting, and compilation straightforward.