Qualitative methods in quantum theory

A.B. Migdal

This unique book, written by a leading Soviet theorist, is not a textbook of quantum mechanics but rather a compendium of the "tricks of the trade"-the methods that all practicing theoretical physicists use but few have set down in writing.

Thomas Bittner

This paper investigates quantized mereology, which merges quantum information theory with classical mereology, the formal analysis of the part-whole relationship. It emphasizes that information about crisp mereological relations is captured by classical bits, whereas mereological vagueness involves the use of quantum bits, or qubits, to capture mereological information. Transitioning from classical bits to qubits offers a new understanding of part-whole relations among entities that are subject to mereological vagueness. This paper methodically studies the quantized mereology that arises from the classical RCC5 formalism, one of the most widely studied formalisms in Qualitative Reasoning (QR), a subfield of Artificial Intelligence. The argument is made that this method can be extended to quantize more sophisticated QR formalisms, mirroring how strategies are used in physics to transition from classical to quantum systems. The study explores: (i) the conversion of bits to qubits while understanding that these (qu)bits convey mereological information; (ii) the representation of qubit states via set partitions, acknowledging that set theory aligns more closely with classical logic than with the complex vector spaces employed in quantum physics; (iii) demonstrating that classical QR formalisms can be seen as special cases within quantized formalisms; and (iv) showing that qubits more effectively encapsulate information about vague phenomena.

Wolfgang Yourgrau, Alwyn van der Merwe, Alfred Landé

Dominik Domin

Studying complex molecular systems, whether in the gas or a condensed phase, requires highly accurate quantum chemistry methods whose computational effort remains tractable when treating realistic systems. Commonly used ab initio methods such as Coupled Cluster (CC) or Density Functional Theory (DFT) generally provide reliable results when the underlying approximations and parameterizations are appropriate for the systems being studied. Among the less popular quantum chemistry methods, Valence Bond (VB) theory and Quantum Monte Carlo (QMC) methods, each provides different unique advantages and disadvantages. Ab initio VB, while usually only qualitative for energetic properties such as enthalpies of formation, has the distinct advantage of providing very compact wave functions that can be readily mapped into the intuitive Lewis structures that chemists very often use when qualitatively describing the valence electronic structure of atoms and molecules. QMC using trial wave functions based on multireference ab initio quantum methods can give some of the most accurate energies and related properties, however, this is often at a great computational cost. Furthermore, the large wave function expansions in the trial function are often difficult to qualitatively interpret. In this lecture, we will present the Valence-Bond Quantum Monte Carlo methods (VB-QMC) which retain the interpretability of VB and the high accuracy of QMC. We will show a few applications which demonstrate their accuracy for molecules in the gas phase and we will examine areas where innovations could be made.

Robert K. Clifton