What the foundations of quantum computer science teach us about chemistry

Grid-based methods for chemistry simulations on a quantum computer

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

Case-Based and Quantum Classification for ERP-Based Brain-Computer Interfaces

Low transfer rates are a major bottleneck for brain-computer interfaces based on electroencephalography (EEG). This problem has led to the development of more robust and accurate classifiers. In this study, we investigated the performance of variational quantum, quantum-enhanced support vector, and hypergraph case-based reasoning classifiers in the binary classification of EEG data from a P300 experiment. On the one hand, quantum classification is a promising technology to reduce computational time and improve learning outcomes. On the other hand, case-based reasoning has an excellent potential to simplify the preprocessing steps of EEG analysis. We found that the balanced training (prediction) accuracy of each of these three classifiers was 56.95 (51.83), 83.17 (50.25), and 71.10% (52.04%), respectively. In addition, case-based reasoning performed significantly lower with a simplified (49.78%) preprocessing pipeline. These results demonstrated that all classifiers were able to learn from the data and that quantum classification of EEG data was implementable; however, more research is required to enable a greater prediction accuracy because none of the classifiers were able to generalize from the data. This could be achieved by improving the configuration of the quantum classifiers (e.g., increasing the number of shots) and increasing the number of trials for hypergraph case-based reasoning classifiers through transfer learning.