Talk:Mølmer–Sørensen gate

The gate described is not unitary and thus can't be a valid quantum gate. This must be a mistake. — Preceding unsigned comment added by 134.160.214.34 (talk) 07:37, 20 February 2018 (UTC)

The gate exploits a transient coupling between the qubit states and the phonon/vibrational modes of the trapped ions. If the operation is not tuned correctly, there will be residual entanglement to those modes. Once tracing over the phonon modes, this will result in an effective nonunitary evolution of the qubits. However, this effect can be very small and in many cases tuned to exactly zero. 50.204.78.3 (talk) 14:23, 29 November 2022 (UTC)

The "gate" in this context is not the Molmer Sorensen Hamiltonian H but rather the propagator which is calculated from the Hamiltonian via the Schrodinger equation. The general solution is given by the Magnus expansion $U(t)=e^{\sum _{l=1}^{\infty }M_{l}(t)}$. If the exponent is skew hermitian then U is unitary here, and you can check here the nth term of the Magnus expansion will be skew hermitian if the Hamiltonian is hermitian. So the gate is unitary. Penrose sachdev (talk) 10:52, 12 February 2024 (UTC)

What is the actual definition of this gate??

IBM Qiskit defines Mølmer Sorensens gate as RXX and defines a general MG gate for three qubits. However this article talks about the original one that seems not to be parametrized and equivalent to Ryy to some angle?? ReyHahn (talk) 16:01, 14 September 2022 (UTC)

The original paper, cirq, IBM and other articles contain multiple definitions of the MG gate. I suggest changing the name to Mølmer–Sørensen gates.--ReyHahn (talk) 16:54, 14 September 2022 (UTC)

Different definitions:

• Wiki article, definition 1: $Ryy(\pi /2)$.
• Wiki article, definition 2: $Rxx(\pi /2)$.
• Qiskit MSGate [1]: $Rxx(\theta )$.
• Qiskit GMSGate [2]: three qubit parametrized gate with $Rxx(\theta )$ rotations on two pair of qubits.
• Q-Control [3]: multi-qubit gate that applies $Rxx(\theta )$.
• IonQ/Cirq MS gate [4]: $Rxx(\pi /2)$.
• IonQ/Cirq MSGate gate [5]: $Rxx(\pi /2)$ but with some parametrized phases in the antidiagonal.
• Original paper (PRL 1999): $Ryy(\theta )$?.
• Parametrized gate that can mean any of the above: Martinez-Garcia et al 2021
• Other papers with $Rxx(\theta )$: Wang et al 2021
• Other papers with $Rxx(\pi /2)$: Brickman et al 2005, Haffner et al 2008
• Other papers with $Ryy(\theta )$: Martin et al 2021

What do you think is the most fitting definition to encompass all of them? Are Mølmer-Sørensen gates the same as the Ising gates? Does it even refer to a gate or to a procedure?--ReyHahn (talk) 19:13, 24 September 2022 (UTC)

These definitions are all applications of the original "MS Gate" presented by Molmer and Sorenson in 1999. We can define the original MS gate as the simultaneous application of a red and blue sideband, each symmetrically detuned from the resonance of a motional mode of a trapped ion chain. The most general MS Hamiltonian is written in terms of the phase angle of each laser field. Depending on how you set those phases, you can get XX or YY as the rotation angle. The gate is typically written as the sum of XX interactions on all qubit pairs, and an MS gate on 2 qubits reduces to the RXX gate. You can apply the gate for any duration; some of the above references are referring to the gate as being at the time of maximal entanglement (,$\pi /2$), but it doesn't have to be. Since the introduction of the original MS gate, there have been many proposals for ways to alter it to increase gate fidelities, so you will see versions that are modulated by allowing the laser phases/intensities or detuning to vary with time, or some people have created generalizations to include more tones as in [1]. Other platforms like superconducting qubits have started using 'MS-type' or 'MS-like' gates, which may mean 'Ising-type interaction' or may mean 'uses a bichromatic driving field to employ a shared mode between qubits'. But I think this article should mostly refer to the original MS gate as presented by Molmer and Sorensen for trapped ions; it could have sections titled "Generalizations of the MS Gate" and "MS-like Gates in Other Platforms"

[1] https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.121.180502 152.3.43.43 (talk) 21:33, 8 November 2022 (UTC)

Correction: The "original" MS gate would actually include Molmer and Sorensen's papers from both 1999 and 2000. Both are the same bichromatic laser field, but in 1999, M & S looked only at the slow gate (weak field) regime ($\eta \Omega \ll \nu -\delta$) where negligible phonon population is transferred throughout the gate. In 2000 they considered the fast gate (strong field) regime ($\Omega \ll \delta ,\nu -\delta \ll \delta$) where decoupling from motion has to be done intentionally by choosing parameters such that the gate ends at the correct location in phase space [1].

[1] https://arxiv.org/pdf/quant-ph/0002024.pdf 152.3.43.43 (talk) 21:59, 8 November 2022 (UTC)

Could you specify if MS gate is a scheme/procedure/protocol to make quantum gates? Or is it specifically a quantum gate per se like CNOT?--ReyHahn (talk) 19:45, 9 November 2022 (UTC)

Any quantum gate that uses the procedure described in Molmer and Sorensen's paper from 2000 is an MS gate. The term is used interchangeably to talk about the implementation procedure and the resulting gate Mddonofr (talk) 20:54, 9 November 2022 (UTC)

I'll keep updating the page throughout this week. I looked for it 6 years ago when I started in an ion trapping lab, and I can't believe it still doesn't exist haha. Mddonofr (talk) 20:56, 9 November 2022 (UTC)

I attempted to update a link to our MS gate definition after a colleague noticed it failed verification. Feel free to restore it if I've messed anything up. Re: the above conversation, agree with the summary that MS is best described as a procedure for developing gates, though it's used as shorthand for gates developed that way. I am not a physicist though, just a software engineer, so take w/ a grain of salt DonovanIonQ (talk) 23:51, 28 November 2022 (UTC)