Molmer Sorensen Gate Trapped Ions

Short answer: The Molmer-Sorensen gate is an entangling gate for trapped ions, proposed by Anders Sorensen and Klaus Molmer in 1998 and 2000 papers, that uses bichromatic light and virtual vibrational excitations so the gate does not depend on the ions' thermal motion. A 2018 Physical Review Letters paper generalized it with multitone drives and demonstrated resilient versions on strontium ions. The first two sources are theory proposals, and the third is a laboratory demonstration.

The proposal

The 1998 paper, "Quantum computation with ions in thermal motion", proposes an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. In its abstract, transition paths involving unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence, the authors say, quantum computation becomes feasible with ions whose vibrations are strongly coupled to a thermal reservoir. The arXiv comments say a revised version demonstrates that the gate is insensitive to heating and shows how to perform a controlled-NOT with it.

The 2000 analysis

The follow-up paper, "Entanglement and quantum computation with ions in thermal motion", says that with bichromatic fields it is possible to deterministically produce entangled states of trapped ions. It presents a unified analysis of this process for weak and strong fields, and for slow and fast gates, and derives simple expressions for the fidelity of creating maximally entangled states of two or an arbitrary number of ions under non-ideal conditions.

The paper explains that its bichromatic scheme is a realization of an earlier proposal by Milburn, and that gate operation more rapid than concluded in an earlier paper is possible. It says the propagator can prepare maximally entangled states of any number of ions, of the form (|gg...g> + e^(i phi)|ee...e>), from a string of ions initially in |gg...g>, and that they may be produced even without experimental access to individual ions in the trap.

Making the gate robust, 2018

A 2018 Physical Review Letters paper says high-fidelity two-qubit entangling gates are a necessary building block for a universal quantum computer, and that such gates have been demonstrated on trapped-ion qubits but control errors and noise in gate parameters may still reduce fidelity. The authors propose and demonstrate a general family of two-qubit entangling gates robust to different sources of noise and control errors. These gates generalize the Molmer-Sorensen gate by using multitone drives. They implemented several of them on strontium-88 ions in a linear Paul trap and verified their resilience. The abstract does not give a fidelity number, so we do not quote one.

What this does not tell you

These sources do not give gate fidelities for any particular machine, and they do not say how the gate is used in any commercial system. The 1998 and 2000 papers are proposals and analysis.

FAQ

What is the Molmer-Sorensen gate?

An entangling gate for trapped ions, using bichromatic light and virtual vibrational excitations, proposed by Sorensen and Molmer.

Why does thermal motion matter?

The authors say the gate's dependence on vibrational quantum numbers cancels, so it can work with ions whose vibrations are strongly coupled to a thermal reservoir.

Can it entangle more than two ions?

The 2000 paper says it can prepare maximally entangled states of any number of ions.

What did the 2018 paper change?

It generalized the gate with multitone drives to make it robust to noise and control errors, and demonstrated this on strontium-88 ions.

Did these papers measure a gate fidelity?

The abstracts we reviewed do not give one.