Pauli exclusion principle

About: Pauli exclusion principle is a research topic. Over the lifetime, 5551 publications have been published within this topic receiving 131561 citations. The topic is also known as: exclusion principle (physics) & principle of exclusion (quantum mechanics).

Fermionic Superfluidity with Imbalanced Spin Populations

Abstract: We established superfluidity in a two-state mixture of ultracold fermionic atoms with imbalanced state populations. This study relates to the long-standing debate about the nature of the superfluid state in Fermi systems. Indicators for superfluidity were condensates of fermion pairs and vortices in rotating clouds. For strong interactions, near a Feshbach resonance, superfluidity was observed for a broad range of population imbalances. We mapped out the superfluid regime as a function of interaction strength and population imbalance and characterized the quantum phase transition to the normal state, known as the Pauli limit of superfluidity.

Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory

Abstract: The standard Pauli Hamiltonian is highly singular for Coulomb potentials near the nuclei of the atoms. It is shown that the theory of effective Hamiltonians allows the determination of Pauli-like Hamiltonians that are regular enough to be used in variational calculations. A numerical illustration is given for hydrogenic atoms with atomic number varying from Z = 1 to Z = 86. These calculations yield relativistic correction potentials which are used for studying the series of neutral rare gas atoms. Our approach opens the way for accurate two-component calculations for molecules.

Towards an exact description of electronic wavefunctions in real solids

Abstract: The properties of all materials arise largely from the quantum mechanics of their constituent electrons under the influence of the electric field of the nuclei. The solution of the underlying many-electron Schrodinger equation is a ‘non-polynomial hard’ problem, owing to the complex interplay of kinetic energy, electron–electron repulsion and the Pauli exclusion principle. The dominant computational method for describing such systems has been density functional theory. Quantum-chemical methods—based on an explicit ansatz for the many-electron wavefunctions and, hence, potentially more accurate—have not been fully explored in the solid state owing to their computational complexity, which ranges from strongly exponential to high-order polynomial in system size. Here we report the application of an exact technique, full configuration interaction quantum Monte Carlo to a variety of real solids, providing reference many-electron energies that are used to rigorously benchmark the standard hierarchy of quantum-chemical techniques, up to the ‘gold standard’ coupled-cluster ansatz, including single, double and perturbative triple particle–hole excitation operators. We show the errors in cohesive energies predicted by this method to be small, indicating the potential of this computationally polynomial scaling technique to tackle current solid-state problems. Recent developments that reduce the computational cost and scaling of wavefunction-based quantum-chemical techniques open the way to the successful application of such techniques to a variety of real-world solids. Computational descriptions of solid-state materials are currently dominated by methods based on density functional theory. An attractive and potentially more accurate approach would be to adopt the wavefunction-based methods of quantum chemistry, although these have not received as much attention because of the computational complexities involved. Now George Booth and colleagues show how recent developments that serve to reduce the computational cost and scaling of such quantum-chemical techniques open the way to their successful application to a variety of real-world solids.

Classification with Quantum Neural Networks on Near Term Processors

Abstract: We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network's predictor of the binary label of the input state. First we look at classifying classical data sets which consist of n-bit strings with binary labels. The input quantum state is an n-bit computational basis state corresponding to a sample string. We show how to design a circuit made from two qubit unitaries that can correctly represent the label of any Boolean function of n bits. For certain label functions the circuit is exponentially long. We introduce parameter dependent unitaries that can be adapted by supervised learning of labeled data. We study an example of real world data consisting of downsampled images of handwritten digits each of which has been labeled as one of two distinct digits. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.