quantum gate directory

Qubits: $n$ Parameters: $n(n-1)/2$

SDK Support

SDK	Name
Qiskit	qiskit.circuit.library.MSGate
PennyLane	— ⓘ
Cirq	cirq.MSGate ⓘ
Q#	—
PyQuil	—
Braket	braket.circuits.gates.MS ⓘ
BQSKit	bqskit.ir.gates.XXGate ⓘ
Qibo	qibo.gates.MS ⓘ
pytket	pytket.circuit.OpType.AAMS ⓘ
Stim	SQRT_XX ⓘ
OpenQASM	—

Reference

Multiparticle Entanglement of Hot Trapped Ions (1999)

The Mølmer-Sørensen (MS) gate acts on $n$ qubits and, for $n = 2$, reduces to an $XX$ rotation. In full generality the MS gate (sometimes referred to as global MS or GMS) takes $n(n-1)/2$ parameters $\chi_{ij}$.

$$ \mathrm{MS}(\chi_{ij}) = \exp\left(-i \sum_{i=1}^n\sum_{j=i+1}^n X_i\otimes X_j \, \chi_{ij} / 2\right) $$

Where $X_i$ denotes a Pauli X on qubit $i$.

Properties

• For two qubits, $\mathrm{MS}(\chi) = R_{xx}(\chi)$.
• Entangling for nontrivial angles; $\chi = \pi/2$ yields a maximally entangling gate.
• Symmetric under qubit exchange in the two-qubit case.

Usage

• Native two-qubit entangling gate in trapped-ion hardware.
• Building blocks for GHZ states, parity checks, and variational layers.

References

• Use of global interactions in efficient quantum circuit constructions