Related papers: Hamiltonian Formalism for Comparing Quantum and Cl…
Formal languages are essential for computer programming and are constructed to be easily processed by computers. In contrast, natural languages are much more challenging and instigated the field of Natural Language Processing (NLP). One…
AIXI is a widely studied model of artificial general intelligence (AGI) based upon principles of induction and reinforcement learning. However, AIXI is fundamentally classical in nature - as are the environments in which it is modelled.…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the…
Quantum dynamics simulations of reactive molecular processes are commonly performed in a low-dimensional space spanned by highly optimized reactive coordinates. Usually, these sets of reactive coordinates consist of non-linear coordinates.…
We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to…
We introduce a Hamiltonian-based quantum feature extraction method that generates complex features via the dynamics of $k$-local many-body spins Hamiltonians, enhancing machine learning performance. Classical feature vectors are embedded…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with…
The classical Coriolis force finds its quantum analogue in the difference $\Sigma(t)=H(t)-G(t)$ where the ``true'', observable Hamiltonian $H(t)$ represents the instantaneous energy. The other, ``false'' Hamiltonian $G(t)$ generates the…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…
Free energy fixes the maximum work of a thermodynamic process once the state and Hamiltonian are specified. A work-extraction task asks a different question: how much average work can a single device realize across several preparations and…