controlledSWAP

The controlled-SWAP gate, often abbreviated as C-SWAP or Fredkin gate, is a fundamental three-qubit quantum gate. It acts as a conditional swap operation. Its function is as follows: if the control qubit is in the state |1⟩, it performs a SWAP operation on the other two qubits. If the control qubit is in the state |0⟩, it leaves the other two qubits unchanged. The controlled-SWAP gate is a universal quantum gate, meaning that any quantum computation can be constructed using only controlled-SWAP gates and single-qubit gates.

Mathematically, the controlled-SWAP gate can be represented by a 3x3 matrix. For qubits A (control), B, and C, the action of the C-SWAP is:

|0⟩|x⟩|y⟩ → |0⟩|x⟩|y⟩

|1⟩|x⟩|y⟩ → |1⟩|y⟩|x⟩

where |x⟩ and |y⟩ represent any valid state for qubits B and C, respectively.

The controlled-SWAP gate plays a crucial role in various quantum algorithms and protocols. It is instrumental in implementing quantum algorithms that require conditional logic, such as quantum sorting algorithms and fault-tolerant quantum computation. Its ability to conditionally permute states makes it a powerful tool for manipulating quantum information in a controlled manner. While it requires three qubits, its universality makes it a building block for more complex quantum operations and circuits.