Related papers: Student difficulties with representations of quant…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
Despite numerous advances in the field and a seemingly ever-increasing amount of investment, we are still some years away from seeing a production quantum computer in action. However, it is possible to make some educated guesses about the…
Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…
The problem of observables in classical and quantum gravity is a long-standing one. It is sometimes argued that observable quantities should be diffeomorphsm invariant, following the philosophy of Dirac. We argue that diffeomorphism…
Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
Commutator anomalies obstruct solving the Wheeler-DeWitt constraint equation in Dirac quantization of quantum gravity-matter theory. When the obstruction is removed, there result quantal modifications to the constraints. The same classical…
A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to…
Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving a variety of machine learning tasks. Variational methods that use quantum resources of imperfect quantum devices with the help of classical…
Fermi-Dirac machines were proposed recently as an approach to solving semidefinite optimization problems on quantum computers. Here, we reinterpret them as canonical quantizations of classical neurons. By viewing a classical neuron as an…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Ambiguity in the contact between laboratory instruments and equations of quantum mechanics is formulated in terms of responses of the instruments to commands transmitted to them by a Classical digital Process-control Computer (CPC); in this…
Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman…
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical…
Quantum error avoiding codes are constructed by exploiting a geometric interpretation of the algebra of measurements of an open quantum system. The notion of a generalized Dirac operator is introduced and used to naturally construct…
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we…