Abstract The computational treatment of many‐electron systems capable of exchanging electrons and nuclei with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this Progress Report, an overview of problems in current materials science and chemical physics is presented where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and quantum/classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness, and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.
Abstract The computational treatment of many‐electron systems capable of exchanging electrons and nuclei with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this Progress Report, an overview of problems in current materials science and chemical physics is presented where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and quantum/classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness, and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman's idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.
Quantum many-body calculation methods, including exact diagonalization, quantum Monte Carlo, density matrix and tensor renormalization, and dynamic mean field theory, as well as emerging methods harnessing the power of artificial intelligence and quantum computing, can be used to accurately and efficiently calculate the physical properties of correlated quantum many-body systems. The quantum particles in the interacting, non-perturbative many-body system are highly entangled, and the mean field theory often lacks sufficient accuracy or may even break down for certain problems. It is thus very necessary to develop new methods for studying the exotic states and emergent phenomena in correlated systems, such as high-temperature superconductivity and frustrated quantum magnetism. Recently, the rapid progress in the field of many-body calculation has shown the characteristics of interdisciplinary cross, and there is increasingly significant interplay and integration with machine learning, materials science, quantum simulation and computation, among other fields. This paper outlines the brief history of many-body calculations, major approaches and their current status, as well as main challenges in this field.
Precise prediction and control of chemical reactions and material propertiesthe central goal of precision chemistrytruly rely on accurate and efficient theoretical modeling of chemical systems. In recent years, significant progress has been made in theoretical and computational chemistry. Especially, interdisciplinary studies in the direction of the two emerging computational frontiers, artificial intelligence and quantum computation, are revolutionizing this field. Expressive neural networks can be used to represent many-electron wave functions with high accuracy, capturing strong correlations with a favorable computational cost compared to other methods. Leveraging quantum computation in quantum chemistry is also expected to deliver a quantum advantage in problems including electronic structure calculations. With artificial intelligence and quantum computation, we expect to establish a unified, high-precision, and scalable computational foundation for generating accurate quantum chemical data essential for precision chemistry.
The electron liquid paradigm is at the basis of most of our current understanding of the physical properties of electronic systems. Quite remarkably, the latter are nowadays at the intersection of the most exciting areas of science: materials science, quantum chemistry, nano-electronics, biology, and quantum computation. Accordingly, its importance can hardly be overestimated. During the past 20 years the field has witnessed momentous developments, which are partly covered in this new volume. Advances in semiconductor technology have allowed the realizations of ultra-pure electron liquids whose density, unlike that of the ones spontaneously occurring in nature, can be tuned by electrical means, allowing a systematic exploration of both strongly and weakly correlated regimes. Most of these system are two- or even one-dimensional, and can be coupled together in the form of multi-layers or multi-wires, opening vast observational possibilities. On the theoretical side, quantum Monte Carlo methods have allowed an essentially exact determination of the ground-state energy of the electron liquid, and have provided partial answers to the still open question of the structure of its phase diagram. Starting from the 1980s some truly revolutionary concepts have emerged, which are well represented in this volume.
Abstract Molecular science is governed by the dynamics of electrons and atomic nuclei, and by their interactions with electromagnetic fields. A faithful physicochemical understanding of these processes is crucial for the design and synthesis of chemicals and materials of value for our society and economy. Although some problems in this field can be adequately addressed by classical mechanics, many demand an explicit quantum mechanical description. Such quantum problems require a representation of wave functions that grows exponentially with system size and therefore should naturally benefit from quantum computation on a number of logical qubits that scales only linearly with system size. In this perspective, we elaborate on the potential benefits of quantum computing in the molecular sciences, i.e., in molecular physics, chemistry, biochemistry, and materials science.