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As the year-to-year gains in speeds of classical computers continue to taper off, computational chemists are increasingly examining quantum computing as a possible route to achieve greater computational performance. Quantum computers, built upon the properties of superposition, interference, and entanglement of quantum bits, offer, in principle, the possibility to outperform classical computers for solving many important classes of problems. In the field of chemistry, quantum algorithm development offers promising propositions for solving classically intractable problems in areas such as electronic structure, chemical quantum dynamics, spectroscopy, and cheminformatics. However, physical implementations of quantum computers are still in their infancy and have yet to outperform classical computers for useful computations. Still, quantum software development for chemistry is a highly active area of research. In this perspective, we summarize recent progress in the areas of quantum computing algorithms, hardware, and software, and we describe the challenges that remain for useful implementations of quantum computing for chemical applications. 

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon.