# Mølmer–Sørensen gate

The Mølmer–Sørensen gate is a two qubit gate used in quantum computing. It was proposed by Klaus Mølmer and Anders Sørensen.[1]

## Implementation

To implement the gate, two ions are irradiated with a bichromatic laser field with frequencies ${\displaystyle \omega _{0}\pm (\omega _{\text{qubit}}+\delta )}$, which, depending on the interaction time, produces the states

{\displaystyle {\begin{aligned}\mid ee\rangle \rightarrow (|ee\rangle +i|gg\rangle )/{\sqrt {2}}\\\mid eg\rangle \rightarrow (|eg\rangle +i|ge\rangle )/{\sqrt {2}}\\\mid ge\rangle \rightarrow (|ge\rangle +i|eg\rangle )/{\sqrt {2}}\\\mid gg\rangle \rightarrow (|gg\rangle +i|ee\rangle )/{\sqrt {2}}\end{aligned}}}

The above can then be shown to produce a universal set of gates. The Mølmer–Sørensen gate has the advantage that it does not fail if the ions were not cooled completely to the ground state, and it does not require the ions to be individually addressed.[2] An experiment was done by P.C. Haljan, K. A. Brickman, L. Deslauriers, P.J. Lee, and C. Monroe where this gate was used to produce all four Bell states and to implement Grover's algorithm successfully.[3]

## References

1. ^ Sørensen, Anders; Mølmer, Klaus (March 1, 1999). "Multi-particle entanglement of hot trapped ions". Physical Review Letters. 82 (9): 1835. arXiv:quant-ph/9810040. Bibcode:1999PhRvL..82.1835M. doi:10.1103/PhysRevLett.82.1835.
2. ^ HAFFNER, H; ROOS, C; BLATT, R (2008). "Quantum computing with trapped ions". Physics Reports. 469 (4): 155–203. arXiv:0809.4368. Bibcode:2008PhR...469..155H. doi:10.1016/j.physrep.2008.09.003.
3. ^ Haljan, P. C. (2005). "Spin-Dependent Forces on Trapped Ions for Phase-Stable Quantum Gates and Entangled States of Spin and Motion". Physical Review Letters. 94 (15). arXiv:quant-ph/0411068. Bibcode:2005PhRvL..94o3602H. doi:10.1103/physrevlett.94.153602.