A thread on the Cirac-Zoller gate: why it is important and why it is never used. (1/n)
In 1995, ions were clearly a good choice for a qubit. The internal states were known to be very coherent and are still used to this day to build incredibly precise atomic clocks (2/n).
The problem is how to couple the internal states of the ions together to do conditional logic. In an ion trap, ions stay microns apart due to the Coulomb repulsion and at that distance the coupling between internal states is very weak. (3/n)
Aside: One of my favorite experiments shows the coupling between the magnetic dipoles of the spins on two separated ions. Ozeri and his group used all possible tricks to remove magnetic field noise to show this. (arxiv.org/abs/1312.4881). The interaction is mHz. (4/n)
The Coulomb repulsion leads to shared modes of ion motion. The Cirac-Zoller gate uses these shared modes as an auxillary qubit by applying operations that keeps the motional state in |0> and |1>. (5/n)
It requires that we are in the ground motional state |0> and relies on the fact that there is no |-1> state of a quantum harmonic oscillator. It uses another odd property of quantum mechanics that I can rotate back to the same state and pick up a phase of -1. (6/n)
This phase doesn't do anything unless it is conditional on another part of the quantum system. In this case, it is conditional on the motion being in the state |1>and only works when the atom is in a specific state. We can put these pieces together to make a Controlled-Z. (7/n)
A few single-qubit operations and we have the more familiar CNOT. The basic idea was used immediately to perform a logic operation between one atom and the motion journals.aps.org/prl/abstract/1… (8/n)
The two ion Cirac-Zoller gate wasn't demonstrated for another 8 years. nature.com/articles/natur…
Why? (9/n)
Why? (9/n)
The problem is preparing the motion in the |0> state and keeping it cold. Ion trappers are quite good at preparing this state but it still can have a few percent population in the excited state. This becomes the hard limit on your two-qubit gate fidelity. (10/n)
Lucky for us in 1998 there was a series of work developing two-qubit gates that are independent of the specific ion motional state
arxiv.org/abs/quant-ph/9…
arxiv.org/abs/quant-ph/9…
arxiv.org/abs/quant-ph/9…
(11/n)
arxiv.org/abs/quant-ph/9…
arxiv.org/abs/quant-ph/9…
arxiv.org/abs/quant-ph/9…
(11/n)
The first gate of this type was the Geometric Phase Gate which occurred the same year at the experimental Cirac Zoller gate
nature.com/articles/natur… (12/n)
nature.com/articles/natur… (12/n)
Since then the Molmer-Sorensen approach has been the most popular and variations have led to very high-fidelity two qubit gates. journals.aps.org/prl/abstract/1… (13/n)
From my perspective, the Molmer-Sorensen gate is an example of an effective quantum technology. It is so good everyone adopts it. Lately even neutral atoms and superconductors. (14/n)
How does it work in ions? It takes advantage of the other quantum part of a quantum harmonic oscillator: position and momentum don't commute. As a result, a trajectory in phase space that goes back to the same point can generate a phase. (15/n)
Again normally we cannot see this phase. What these gates do is make the trajectory dependent on the internal states of the ions. This maps the phase to the ion states and naturally leads to an Ising type coupling between the qubits. (16/n)
There has lately been a lot of work on optimizing these gates in the community. Here are some designs and examples from @DukeEngineering #DukeQuantum
arxiv.org/abs/1708.08039
arxiv.org/abs/1808.02555
arxiv.org/abs/1905.10421
arxiv.org/abs/2003.12430 (17/17)
arxiv.org/abs/1708.08039
arxiv.org/abs/1808.02555
arxiv.org/abs/1905.10421
arxiv.org/abs/2003.12430 (17/17)
