Molecular Quantum Error Correction

Quantum computing has the potential to solve computational problems that are not accessible to current computers. However, any implementation will be prone to noise and it is believed that quantum error correction (QEC) techniques will be required to run long algorithms. Such correction procedures encode information redundantly, usually spreading out information onto multiple particles. This redundancy causes a resource overhead which is believed to be prohibitively large for near-term quantum computers. Recently, a family of efficient QEC codes for encoding quantum information redundantly in a single molecule has been proposed. Within this project, we aim to identify, analyze, and demonstrate efficient implementations of quantum error correction with single molecules. This project will lay the experimental and theoretical groundwork for such an efficient QEC scheme based on molecular external degrees of freedom. We aim to develop a fault-tolerant framework to create non-classical states and readout complex observables such as error syndromes. We will also explore mechanisms that enable fault-tolerant quantum operations between two molecules, each encoding a logical qubit. The experiment consists of an ion trap quantum computer, in which atomic and molecular ions are co-trapped. Quantum logic techniques that transfer the exquisite control over atomic ions onto the co-trapped molecules will be utilized to prepare the molecules in a pure state and to retrieve information on the error processes. We plan to use frequency comb spectroscopy techniques to access multiple external degrees of freedom of the molecule. An experimentally feasible, resource efficient QEC scheme can lay the groundwork for a new QEC mindset, transforming the entire quantum computing landscape. The combination of robust quantum states with molecular systems might drastically improve precision experiments searching for new physics, such as measuring the electron dipole moment. And creating robust states of molecular degrees of freedom can serve as the basis to control state-selective chemical reactions, opening new research avenues in physics, chemistry, and biology.

Quantum computing, where the information and the operations which act on it are quantum in nature, enable solvability of certain classes of problems not accessible to existing computers. Experiments which attempt to harness this potential are subject to noise induced by the environment which limits the size of computations which can be performed. Quantum error correction (QEC) can protect the information from such noise. We investigated whether it is possible to encode quantum information in how molecules rotate. We developed strategies to protect such encoded information from the noise induced by thermal background radiation. We simulated QEC strategies for codes which were recently developed in 2023 by S. Jain, et al. In these simulations, we found that QEC can protect the encoded information such that it survives for longer than if left unprotected. We developed experimental capabilities to attempt implementation of QEC in a molecular ion trapped in a vacuum chamber. These techniques will ultimately enable the preparation of an initial rotational state and correction of this state when it is perturbed by the environment. The techniques in development include frequency comb Raman, continuous-wave (CW) Raman, and quantum logic spectroscopy. A frequency comb is a laser system whose spectrum has many equally-spaced narrow lines. A Raman process involves driving transitions in an atom or molecule via a two-photon process, where the energy of the transition is related to the frequency difference of the two photons. Frequency comb Raman makes use of a frequency comb to manipulate the rotation of molecules via Raman interactions and can access frequency differences up to a few terahertz. This can enable transitions between rotational states in many molecules. We set up such a system and tested it by driving single-beam Raman transitions between electronic states in a calcium ion. CW Raman makes use of two branches of a CW laser which are shifted in frequency from each other up to hundreds of megahertz. While this frequency difference is too small to drive rotational transitions in many molecules, it can manipulate magnetic substates, which arise in the presence of a magnetic field. These substates form the basis for encoding logical information in the QEC codes studied in this work. We set up a CW Raman system, however it was not tested before the conclusion of this project. After some preliminary study, we chose the calcium monohydroxide ion as the molecule we would attempt to implement QEC in. As this molecule is largely unstudied, we first characterized its electronic properties insofar as to how light can cause it to change electronic energy levels and break apart, or dissociate. This experiment also verified our experimental system's capabilities to form molecular ions and co-trap them with atomic ions.