Study realizes symmetry-protected molecular qubits based on cold polyatomic molecules

Over the past decades, researchers have been trying to develop increasingly advanced and powerful quantum computers, which could outperform classical computers on some tasks. To attain this, they have been trying to identify new ways to store and manipulate qubits, which are the fundamental units of information in quantum computing systems.

So far, most studies have developed quantum systems that store qubits using superconducting materials, trapped ions, and the spin of electrons confined in quantum dots (i.e., tiny semiconductor-based structures).

Another promising and yet so far rarely explored platform for the storage and manipulation of qubits relies on polar polyatomic molecules, which are molecules with more than two atoms and an uneven distribution of electric charge.

Researchers at the Max Planck Institute for Quantum Optics carried out a study exploring the possibility of storing and measuring quantum superpositions in specific rotational quantum states of these molecules.

Their paper, published in Physical Review Letters, unveils an interesting new avenue for the development of quantum computing and sensing technologies, leveraging the rotational states of cold polyatomic molecules.

“We have already been working with formaldehyde and similar molecules for many years and always knew that the rotational states that we worked with were actually degenerate state pairs corresponding to clockwise and counterclockwise rotation, but we more or less ignored this fact,” Maximilian Löw, first author of the paper, told Phys.org.

“I can still remember that one day Martin Zeppenfeld assembled the molecule team and told us that he had an idea about how to measure coherence between these states by taking advantage of the slight asymmetry of formaldehyde molecules. Of course, from there it was still a long way to go before we could perform the measurements we describe in our paper, but that’s where it all began.”

Löw, Zeppenfeld and their colleagues showed that specific rotational quantum states of polar molecules are particularly suited to store quantum superpositions.

Their recent study built on their knowledge that molecular rotational states with nonzero projection of the angular momentum on the electric field direction come in pairs, a clockwise and a counterclockwise rotating version (i.e., opposite-rotation state pairs), which in many respects have indistinguishable properties.

“For a long time, this was always a bit of an annoyance for us, since, for simplicity, it was convenient to consider each pair of states as a single state, but for completeness we always added a note to our papers that each of our ‘states’ in fact consisted of a pair of states,” Zeppenfeld, senior author of the paper, told Phys.org.

“At some point, I realized, however, that this bug can be considered as a major feature, since a quantum superposition could be basically hidden in these pairs of states, due to their in many ways identical properties, while treating the remaining molecular degrees of freedom independently.”

The idea behind the recent work by Löw, Zeppenfeld and their colleagues is that opposite-rotation state pairs in polar molecules could be used to enable the robust storage of quantum information. This is because the pairing between these states can be considered independent from the remaining molecular degrees of freedom.

“I have written in considerable detail about this idea in a concurrent theoretical publication,” explained Zeppenfeld.

“Realizing that these pairs are interesting is only half the story, however, since for a long time we had no idea how to produce and measure superpositions in these states. At some point, we realized, however, that this would be possible by using the slightly asymmetric nature of formaldehyde.”

The main goal of the recent study was to demonstrate that quantum superpositions can be stored and measured in the opposite-rotation state pairs of formaldehyde molecules. To achieve this, however, they first had to cool down and reliably trap these molecules.

“Before we can even think about coherence measurements we have to cool or at least sufficiently slow down the molecules and trap them,” said Löw.

“The trapping and cooling methods we employ were mostly developed in our group and differ quite a lot from the approaches of most other research groups in the field of cold molecules.

“Our trap, for instance, is an electrostatic trap: as our molecules possess a permanent electric dipole moment, they kind of ‘feel’ (if you excuse this non-scientific language) electric fields which allows us to trap them (if they occupy the right states).”

The unique microstructured electric trap devised and employed by the researchers is well-suited for the trapping and cooling of cold molecules. Nonetheless, they provide insufficient optical access and present large field inhomogeneities, thus they are not the ideal location in which to perform coherence measurements.

“Because of this, we had to become a bit creative with our measurement scheme,” explained Löw.

“By exploiting the slight asymmetric structure of formaldehyde, we used RF radiation to selectively remove molecules in one superposition state of our target state pair from our trap, while leaving the complementary superposition state untouched. This creates a population imbalance between the two.

“When you add an external magnetic field to the mix and check for the population of one of the two states a little while later, you end up with these beautiful oscillation patterns shown in our paper, which prove the existence of coherence between the two superposition states.”

To cool their molecules, the researchers employed a technique known as Optoelectric Sisyphus Cooling, which enables the cooling of formaldehyde and other polar molecules down to very low temperatures. The primary challenge that the researchers had to overcome was to encode quantum superposition in their desired state pairs and then demonstrate the existence of these states experimentally.

Their efforts were successful and could open new possibilities for the future development of quantum computing systems. Specifically, their paper introduces a new paradigm for the realization of multi-qubit quantum computing architectures rooted in single molecules based on quasi-hidden degrees of freedom.

“The main aspect of this architecture is that a single qubit is stored in a molecular degree of freedom which is well isolated from the remaining degrees of freedom, allowing additional qubits to be independently stored and manipulated in the remaining degrees of freedom,” explained Zeppenfeld.

“To make the connection to the rest of the discussion clear, the isolated degree of freedom would be the pairing of the clockwise and counterclockwise rotating states, which is very well isolated due to the in many ways identical properties of both states in each pair. In our paper, we have taken a big step in demonstrating this paradigm by preparing and measuring a quantum superposition in these isolated state pairs.”

A further remarkable achievement of the researchers’ study is that the superposition in their state pairs was found to be extremely robust, given that the environment in their experiment was considerably noisy.

Under similar experimental conditions, a generic electric trap would destroy a superposition between a generic pair of states in less than a nanosecond, due to the distinct electric fields in different parts of the trap.

“While the unique properties of our microstructured electric trap increases the possible coherence time for a generic pair of states to about 100 nanoseconds, the identical dependence on the electric field magnitude for both states in each of our pairs allows us to, in fact, observe coherence times of about 100 microseconds,” said Zeppenfeld.

“Moreover, this is not limited by an actual decoherence, but by the time we are able to keep a given molecule under observation. So, this really shows the robustness of our qubits.”

The researchers hope that their study will inspire further research investigating the potential of the experimental platform they outlined. These efforts could in turn facilitate the development of quantum computing systems based on polar molecules.

“Concerning the implications of our work, my hope is that future research will allow a full implementation of quasi-hidden degrees of freedom as a quantum computing platform to be experimentally demonstrated, including encoding, manipulation and readout of qubits in the remaining molecular degrees of freedom with a qubit simultaneously stored in the quasi-hidden degree of freedom, and quantum gates between the qubit stored in the quasi-hidden degree of freedom and the qubits stored in the remaining degrees of freedom,” said Zeppenfeld.

“This might really help to make polar molecules a competitive platform for quantum computing.”

Unfortunately, Zeppenfeld and his team did not yet receive the funding that would allow them to continue assessing the potential of polar molecules for advancing quantum computing. Nonetheless, other research teams could draw inspiration from their recent paper, contributing to the further validation of their theory and proposed experimental platform.

“Throughout my 20 years working in the field of cold and ultracold molecules, I have regrettably consistently struggled getting new and original (and somewhat exotic) ideas accepted by the scientific community,” said Zeppenfeld.

“However, there is lots of excellent work being performed by other experimental groups on other molecule species, and I hope that they will be willing to try implementing the ideas we have presented.

“Moreover, in a recent theoretical paper, colleagues in Austria and the U.S. discuss how their quite different ideas can be understood in the framework of our own work, i.e., quasi hidden degrees of freedom, and this shows how there is quite a bit of potential to develop off our work in unexpected directions.”

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