Related papers: A Sequence of Quantum Gates
It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the Quantum Yang--Baxter equation via Yang--Baxterization…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first…
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…
We study a linear array of coupled cavities interacting with two level systems and show how to construct individually addressable qubits in this system from the long-lived atom-photon excitations (polaritons) at each site. We derive the…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…
Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
We harness general relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories…
A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one…
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These…
Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
In this second part of the `essay on the completion of quantum theory' we define the {\em unitary setting of completed quantum mechanics}, by adding as intrinsic data to those from Part I (arXiv:1711.08643) the choice of a north pole N and…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
{\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit the same spectrum. Both Hamilton operators play a central role for quantum gates in particular for the case spin-$\frac12$ and the case spin-1. The…