hardware natives n qubits n(n-1)/2 parameters
Mølmer-Sørensen
A native entangling interaction in ion-trap systems based on collective spin-motion coupling.
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
The unitary, drawn
Every entry of the matrix as a disc. The area is the transition probability $|U_{jk}|^2$; the colour and the hand are the phase. Rows are outputs $\langle j|$, columns inputs $|k\rangle$, in the computational basis, shown for $n = 2$. Each parameter has a slider; play runs through the family along the path of the Quirk link ($n = 2,\ \chi = 2\pi t$).
Phase
Disc area $= |U_{jk}|^2$. Hover an entry for its value, or take the JSON.
SDK support
How to call this gate in each framework. Hover a ⓘ for a note; the support matrix compares every gate at once.
| 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 | — |