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What the title says. I was wondering if we can use excited high spin states formed by enhanced intersystem crossing for qubits? like intramolecular quartets formed by a doublet and an intersystem crossing into an excited state triplet+doublet.

In my head, we cannot use them given we can factorise the excited state into a triplet and doublet. Or am I getting this wrong?

A good reference for this is https://pubs.acs.org/doi/10.1021/jacs.1c01620

The energy level diagram for this scheme would look like as attached, I understand the diagram looks like a NV center but simply that doesnt mean its a qubit candidate: enter image description here

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In principle you can, sure. If you're worried about singlet/triplet type stuff, people usually use externally applied fields to tune these things, lift degeneracies, or even create them. I could also write down a model of qubits that has triplets and singlets. But if I apply a field to that model, I once again have nice qubits to use.

Having large separations of energy scales is generally a good thing, which seems to be the case in the diagram you supplied. This only needs to hold in some basis, and for you to be able to manipulate the qubits in that basis. You can apply fields / lasers / whatever to suppress off-diagonal processes in this basis. The idea is similar to adding a Z field to an $\vec{S} \cdot \vec{S}$ Heisenberg term to split the degeneracies so you don't get singlet/triplet but instead get four two-qubit states.

I'll also note that using excited states of atoms as qubits is quite common in the AMO setting. I think there are numerous experiments at JILA (in Boulder), e.g., that use hyperfine levels of atoms to realize multiple qubits in a manner similar to what you've drawn above. These levels are split in certain ways, and couplings to cavity (photon) modes help prevent unwanted processes as needed, or enhance those that are more desirable.

The main questions are what quantum operations you can apply to these qubits (the gate set), how long-lived they are, how robust they are to environmental errors and decoherence, whether they can be manipulated independently, whether they can be measured independently, whether they have native interactions that lead to "cross talk" between states you would otherwise identify with independent qubits, and how many of them you can realize in a single experiment.

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  • $\begingroup$ This is a beautiful answer! Thank you very much for this! It really helped clear out some doubts I had. Cheers! $\endgroup$ Commented Jan 1, 2023 at 17:08
  • $\begingroup$ OK sorry for being a bit late, I was wondering what you meant when you said 'I could also write down a model of qubits that has triplets and singlets. But if I apply a field to that model, I once again have nice qubits to use.' $\endgroup$ Commented Jan 2, 2023 at 14:07
  • $\begingroup$ Oh, I just meant the Heisenberg model I wrote later on $\vec{S} \cdot \vec{S}$, which has degeneracies, while if I add a field $h Z$ to both qubits, I no longer have degeneracies, so I really see that I have 4 unique states (rather than 3 and 1), which is easier to manipulate. $\endgroup$ Commented Jan 2, 2023 at 16:25
  • $\begingroup$ This is just to explain how having triplets/singlets isn't automatically a problem since I can usually remove degeneracies / split levels. $\endgroup$ Commented Jan 2, 2023 at 16:40

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