Related papers: Dynamical quantum determinants and Pfaffians
We study the effects of dynamical imperfections in quantum computers. By considering an explicit example, we identify different regimes ranging from the low-frequency case, where the imperfections can be considered as static but with…
Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…
We use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinite-dimensional separable Hilbert spaces: these were long-missing features, which open the way to a wealth of new…
Recently, the entanglement dynamics of two harmonic oscillators initially prepared in a separable-coherent state was demonstrated to offer a pathway for prime number identification. This article presents a generalized approach and outlines…
We determine explicit generators for a cohomology group constructed from a solution of a fuchsian linear differential equation and describe its relation with cohomology groups with coefficients in a local system. In the parameterized case,…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
A concise and self-contained derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Many previously known results are re-derived, revised, some of them completed or corrected. Using as simple method…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are…
Preliminary results concerning non-quadratic (and non-bijective) transformations that exibit a degree of parentage with the well known Levi-Civita, Kustaanheimo-Stiefel, and Fock transformations are reported in this article. Some of the new…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
We present an overview of the existing methods for computing functional determinants, and outline a possible way forward for Hamiltonians of higher dimensions without radial symmetry.
At the heart of quantum technology development is the control of quantum systems at the level of individual quanta. Mathematically, this is realised through the study of Hamiltonians and the use of methods to solve the dynamics of quantum…
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to \emph{nonabelian} groups…