iSWAP Gate

Swaps two qubits and adds a ninety-degree phase to the exchanged amplitudes, a native entangler on many superconducting chips.

Definition

The iSWAP gate exchanges the states of two qubits while multiplying the swapped |01⟩ and |10⟩ amplitudes by i. It arises naturally from an XX+YY interaction run for a full exchange period, so it is the native two-qubit gate on capacitively coupled and tunable-coupler superconducting devices.

Matrix

iSWAP

Only the single-excitation subspace is affected: |00⟩ and |11⟩ are untouched, while |01⟩ and |10⟩ trade places with an i phase. This makes iSWAP excitation-conserving, useful for particle-number-preserving simulation.

Entangling power

iSWAP is a maximally entangling gate, in the same local-equivalence class as neither CNOT nor SWAP but at its own vertex of the Weyl chamber. A CNOT can be built from a single iSWAP plus single-qubit gates, so no extra entanglers are wasted when compiling to iSWAP-native hardware.

python

import numpy as np
def iswap():
    m = np.eye(4, dtype=complex)
    m[1,1]=0; m[2,2]=0; m[1,2]=1j; m[2,1]=1j
    return m

Uses

Beyond being a native entangler, iSWAP directly implements the full hopping term of the XX+YY exchange, so it is efficient for fermionic and spin-model simulation. Its square root, √iSWAP, is even more common on hardware because a single √iSWAP already suffices with single-qubit gates to build a CNOT. See √iSWAP and XX+YY.