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Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific…
Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we have performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting best-practice…
\emph{Ab initio} computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which…
In the rapidly growing area of quantum information, the Deutsch algorithm is ubiquitous and, in most cases, the first one to be introduced to any student of this relatively new field of research. The reason for this historical relevance…
Accurate and scalable methods for computational quantum chemistry can accelerate research and development in many fields, ranging from drug discovery to advanced material design. Solving the electronic Schrodinger equation is the core…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
We discuss a method of solving the time dependent Schrodinger equation for atoms with two active electrons in a strong laser field, which we used in a previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to calculate…
We present a general theory to treat periodic solids with quantum-chemistry methods. It relies on two main developments: 1) the modeling of a solid as a Clifford torus which is a torus that is both periodic and flat and 2) the introduction…
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of…
Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging…
Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure…
A long-standing goal of science is to accurately solve the Schr\"odinger equation for large molecular systems. The poor scaling of current quantum chemistry algorithms on classical computers imposes an effective limit of about a few dozen…
Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…