# Electronic states of a molecule for qubit in quantum computing

Can electronic states of a molecule be used for representing qubits?

I recently studied quantum computing a little bit with "Quantum Computation and Quantum Information" written by M. A. Nielsen and I. L. Chuang.

They introduced some physical realizations for a quantum computer, and Their qubit representation using spin, charge, photon.

That makes me bring up the question aforementioned.

I searched for some articles about molecular qubits, but I couldn't find stuff about my question. Many papers deal with charge qubits of a quantum dot, and magnetic spin states.

If you know any reference for my question, please notice me.

Also, if you think the idea of using electronic states as qubits is unrealistic, I want to know the reason.

• There are many ways that electronic states can be used as qubits - the most well known is the electronic states of individual ions. Molecular states for quantum computing are more recently also being looked at. For example, here is a proposal to use molecules for quantum computing: arxiv.org/abs/1805.10930 – Harry Levine Jun 14 '18 at 17:42
• @HarryLevine Thank you for your comment. I read the abstract of the linked article of Arxiv, but it says that qubits are represented with nuclear spin states of atoms. What I seek for is the case where electronic states of a molecule like S0, S1 are used for storage qubits. – Patche Jun 14 '18 at 18:12

Some problems that must be addressed before using molecular states:

The Hilbert space is infinite dimensional - so decide on some subspace like $E \leq E_0$ where the eigenstates with $E$ below and above are sufficiently separated in energy. Not too big of a deal.

Figure out the spectrum. If I want to control the system by absorbing photons I should know what $\frac{\Delta E_{ij}}{\hbar}$ as a starting idea of which photons to send in if I want to drive that transition. Conversely if there are stray photons around, I should make sure none of the transitions will get driven by them accidentally. Or at least the probability for that is sufficiently small.

That process continues in more complicated ways as you get more specific about what your enviornment (that can accidentally screw you over) is. While at the same time you want to be able to do the transformations that you actually intended to do when you try to control the system.

A problem with the harmonic oscillator is the equal level spacings so sometimes you try to do a specific thing with $\mid 0 \rangle$ and $\mid 1 \rangle$ but that spacing is the same as $\mid 1 \rangle$ and $\mid 2 \rangle$ so you do something there too. So you want to avoid that sort of problem too.

So using a big molecule can be a terrible idea. It has messy structure and will probably have bad coherence in any reasonable enviornmental conditions.

A small molecule whose low lying eigenstates you already understand is a much better idea.

• Yes. This is what I'm looking forward. Have you seen any article dealing with this kind of molecular qubits? – Patche Jun 15 '18 at 2:21