A quantum circuit is a model for quantum computation in which a computation is broken down into a sequence of quantum gates, which manipulate quantum bits (qubits). Just as classical circuits operate using classical bits (0s and 1s), quantum circuits utilize the principles of quantum mechanics to perform operations on qubits, which can exist in superpositions of states. ### Key Components of a Quantum Circuit: 1. **Qubits**: The basic unit of quantum information, analogous to classical bits.
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A quantum circuit specifies a sequence of operations on a quantum register, usually drawn with wires for qubits and boxes for quantum gates. Reading from input to output gives the order of composition; two gates acting on separate registers combine through a tensor product.
For example, a Hadamard gate on the first qubit followed by a controlled-NOT gate prepares from , making a Bell state. The circuit describes evolution of amplitudes, while the Born rule predicts the statistics of the final measurement.
General circuits can include preparations, measurements, discarded subsystems and classically controlled later operations, as well as unitary gates. Circuit size and depth measure different costs: many independent gates can occupy one layer, whereas a chain of dependent gates requires successive layers. Translating an ideal circuit into hardware also requires a noise and connectivity model.
