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SWAP Gate

The SWAP gate exchanges the quantum states of two qubits, implemented as three consecutive CNOT gates.

What it means

The SWAP gate exchanges the complete quantum states of two qubits: SWAP|ψ⟩|φ⟩ = |φ⟩|ψ⟩.It can be decomposed into three CNOT gates: CNOT(1,2) * CNOT(2,1) * CNOT(1,2).The SWAP gate preserves entanglement and all quantum properties during the exchange.It is essential in quantum circuits where qubit connectivity is limited -- when two qubits that need to interact are not physically adjacent, SWAP gates route quantum information.The square root of SWAP (√SWAP) is also important as it is a universal entangling gate.

Everyday analogy

The SWAP gate is like two people exchanging seats -- each person moves to the other's position, carrying all their belongings (quantum state) with them.
Think of it as swapping two labeled containers without opening them -- the contents are exchanged perfectly.

Common misconceptions

  • SWAP does NOT copy states -- it exchanges them, consistent with no-cloning.
  • SWAP requires 3 CNOTs -- it is not a primitive gate on most hardware and is expensive.

Key takeaways

  • SWAP exchanges the states of two qubits: SWAP|ψ⟩|φ⟩ = |φ⟩|ψ⟩.
  • Decomposed into three CNOT gates.
  • Essential for qubit routing in limited-connectivity architectures.

Check your understanding

How many CNOT gates are needed to implement a SWAP gate?

  1. A.1
  2. B.2
  3. C.3
  4. D.4
Show the answer

Answer: C. 3

Why: A SWAP gate requires exactly 3 CNOT gates for its decomposition.

Builds on

QubitCNOT Gate

Primary source: Barenco et al., Phys. Rev. A 52, 3457 (1995), doi:10.1103/PhysRevA.52.3457

SWAP = 3 CNOT decomposition is an elementary identity.

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