We develop an atomistic, nearest-neighbor sp3s* tight-binding Hamiltonian to investigate the electronic structure of dilute bismide alloys of GaP and GaAs. Using this model, we calculate that the incorporation of dilute concentrations of Bi in GaP introduces Bi-related defect states in the band gap, which interact with the host matrix valence band edge via a Bi composition dependent band anticrossing (BAC) interaction. By extending this analysis to GaBixAs1$-${}x, we demonstrate that the observed strong variation of the band gap (Eg) and spin-orbit-splitting energy ($\Delta${}SO) with Bi composition can be well explained in terms of a BAC interaction between the extended states of the GaAs valence band edge and highly localized Bi-related defect states lying in the valence band, with the change in Eg also having a significant contribution from a conventional alloy reduction in the conduction band edge energy. Our calculated values of Eg and $\Delta${}SO are in good agreement with experiment throughout the investigated composition range (x$\le${}13%). In particular, our calculations reproduce the experimentally observed crossover to an Eg<$\Delta${}SO regime at approximately 10.5% Bi composition in bulk GaBixAs1$-${}x. Recent x-ray spectroscopy measurements have indicated the presence of Bi pairs and clusters even for Bi compositions as low as 2%. We include a systematic study of different Bi nearest-neighbor environments in the alloy to achieve a quantitative understanding of the effect of Bi pairing and clustering on the GaBixAs1$-${}x electronic structure.

Quantum machine learning (QML) has received increasing attention due to its potential to outperform classical machine learning methods in problems such as classification and identification tasks. A subclass of QML methods is quantum generative adversarial networks (QGANs) which have been studied as a quantum counterpart of classical GANs widely used in image manipulation and generation tasks. The existing work on QGANs is still limited to small-scale proof-of-concept examples based on images with significant down-scaling. Here we integrate classical and quantum techniques to propose a new hybrid quantum-classical GAN framework. We demonstrate its superior learning capabilities over existing quantum techniques by generating 28×28 pixels grey-scale images without dimensionality reduction or classical pre/post-processing on multiple classes of the standard MNIST and Fashion MNIST datasets, which achieves comparable results to classical frameworks with three orders of magnitude less trainable generator parameters. To gain further insight into the working of our hybrid approach, we systematically explore the impact of its parameter space by varying the number of qubits, the size of image patches, the number of layers in the generator, the shape of the patches and the choice of prior distribution. Our results show that increasing the quantum generator size generally improves the learning capability of the network. The developed framework provides a foundation for future design of QGANs with optimal parameter set tailored for complex image generation tasks

Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be mitigated by developing higher-quality qubits. Quantum error correction (QEC) will thus be necessary to ensure fault tolerance. QEC protects the logical information by cyclically measuring syndrome information about the errors. An essential part of QEC is the decoder, which uses the syndrome to compute the likely effect of the errors on the logical degrees of freedom and provide a tentative correction. The decoder must be accurate, fast enough to keep pace with the QEC cycle (e.g. on a microsecond timescale for superconducting qubits) and with hard real-time system integration to support logical operations. As such, real-time decoding is essential to realize fault-tolerant quantum computing and to achieve quantum advantage. In this work, we highlight some of the key challenges facing the implementation of real-time decoders while providing a succinct summary of the progress to-date. Furthermore, we lay out our perspective for the future development and provide a possible roadmap for the field of real-time decoding in the next few years. As the quantum hardware is anticipated to scale up, this perspective article will provide a guidance for researchers, focusing on the most pressing issues in real-time decoding and facilitating the development of solutions across quantum, nano and computer science.