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Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field theories have not been formulated so far. To resolve this problem, first, we define what mean-field theory is, independently of a…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
Finding the ground state energy of electrons subject to an external electric field is a fundamental problem in computational chemistry. We prove that this electronic-structure problem, when restricted to a fixed single-particle basis and…
We review the basic ideas of the dynamical mean field theory (DMFT) and some of the insights into the electronic structure of strongly correlated electrons obtained by this method in the context of model Hamiltonians. We then discuss the…
Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works,…
Efficient encoding of electronic operators into qubits is essential for quantum chemistry simulations. The majority of methods map single electron states to qubits, effectively handling electron interactions. Alternatively, pairs of…
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…
We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped…
In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…
The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic…
We investigate the magnetic quantum phase-transitions in bulk correlated metals at the level of dynamical mean-field theory. To this end, we focus on the Hubbard model on a simple cubic lattice as a function of temperature and electronic…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
Advances in quantum computation for electronic structure, and particularly heuristic quantum algorithms, create an ongoing need to characterize the performance and limitations of these methods. Here we discuss some potential pitfalls…
Near-term quantum simulators are mostly based on qubit-based architectures. However, their imperfect nature significantly limits their practical application. The situation is even worse for simulating fermionic systems, which underlie most…
Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the…
Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…