Controlled quantum operation
A controlled quantum operation is a quantum operation applied to target systems only when specified control qubits have required states.
Quantum Programming in Depth
A controlled gate is a quantum gate whose operation on a target system is conditioned on one or more control qubits.
- How it is used
- Constructs block-diagonal operations, CS decompositions, and phase-oracle conversions by conditioning target unitaries on control patterns.
- How deep it goes
- Defines basis-state and superposition behavior, derives matrix decompositions, and extends them to multiple controls through basis-index analysis.
- Examples
- Uses CNOT, controlled X versus controlled −X on |++⟩, CS matrices, and a phase-oracle-to-marking-oracle conversion.
- What you can do after
- Evaluate/understand controlled operations as state transformations and compose them to implement selected matrix blocks or oracle behavior.
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Building Quantum Software with Python
A multicontrolled transformation is a quantum transformation applied to a target qubit only when every specified control qubit has the required control value.
- How it is used
- Limits gate effects to selected amplitude pairs when a circuit must condition a target transformation on one or more qubits.
- How deep it goes
- Descends to Python pair filtering and amplitude recombination, while deferring physical implementation costs and coherence effects.
- Examples
- Uses three-qubit state diagrams, controlled-X swaps, Python simulator functions, and repeated controlled rotations in phase estimation.
- What you can do after
- Apply it via Python state-vector functions that select control-qualified pairs and invoke an existing single-qubit gate transformation.
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Related concepts
- control qubituses · A control qubit is a qubit whose state conditionally determines whether a controlled quantum operation acts on target qubits.
- controlled-Ry gateincludes · A controlled-Ry gate is a controlled rotation gate that applies an Ry rotation to target qubits when its control qubits satisfy the control condition.
- CNOT gateincludes · A CNOT gate is a two-qubit controlled-NOT gate that flips a target qubit when its control qubit is one.
- controlled-on-zero gateincludes · A controlled-on-zero gate applies its target operation when its control qubits are in the zero state.
- arrayuses · An array is an indexed, ordered collection of elements arranged in one or more dimensions, with elements accessed by position.
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