Related papers: On Quantum Iterated Function Systems
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous…
Quantum multipole noise is defined as a family of creation and annihilation operators with commutation relations proportional to derivatives of delta function of difference of the times, $[c^-_n(t),c^+_n(\tau)]\approx \delta^{(n)}(\tau-t)$.…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.
The attractors of iterated function systems are usually obtained as the Hausdorff limit of any non-empty compact subset under iteration. In this note we show that an iterated function system on a boundedly compact metric space has compact,…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…
Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0…
Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also…
We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…
Given bounded selfadjoint operators $A$ and $B$ acting on a Hilbert space $\mathcal{H}$, consider the linear pencil $P(\lambda)=A+\lambda B$, $\lambda\in\mathbb{R}$. The set of parameters $\lambda$ such that $P(\lambda)$ is a positive…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on…