Related papers: Geometric tools of the adiabatic complex WKB metho…
Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of…
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…
Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic…
We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…
We introduce an iterative method to univocally determine the adiabatic expansion of the modes of Dirac fields in spatially homogeneous external backgrounds. We overcome the ambiguities found in previous studies and use this new procedure to…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic…
This article describes a bipedal walking algorithm with inverse kinematics resolution based solely on geometric methods, so that all mathematical concepts are explained from the base, in order to clarify the reason for this solution. To do…
Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic…
The geometric phase stands as a foundational concept in quantum physics, revealing deep connections between geometric structures and quantum dynamical evolution. Unlike dynamical phases, geometric phases exhibit intrinsic resilience to…
We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.
Existing quantum algorithms for quantum chemistry work well near the equilibrium geometry of molecules, but the results can become unstable when the chemical bonds are broken at large atomic distances. For any adiabatic approach, this…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…
We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…
We construct the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields. We…
In open quantum systems theory, reduced models are invaluable for conceptual understanding and computational efficiency. Adiabatic elimination is a useful model reduction method for systems with separated timescales, where a reduced model…
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…