Related papers: Hilbert space-valued Gaussian processes, and quant…
Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the…
We analyze qubit channels by exploiting the possibility of representing two-level quantum systems in terms of characteristic functions. To do so, we use functions of non-commuting variables (Grassmann variables), defined in terms of…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform…
Given a unitary representation $U$ of an Abelian group $G$ and a subgroup $H$, we characterise the positive operator valued quotient group $G/H$ and covariant with respect to $U$.
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
Implementing quantum algorithms is essential for quantum computation. We study the implementation of three quantum algorithms by performing homodyne measurements on a two-dimensional temporal continuous-variable cluster state. We first…
To speed up Gaussian process inference, a number of fast kernel matrix-vector multiplication (MVM) approximation algorithms have been proposed over the years. In this paper, we establish an exact fast kernel MVM algorithm based on exact…
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In…
A new local and gauge invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of a loop expansion in…
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics, we introduce a new family of randomised path developments…
We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…
A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which ``unravels'' the quantum Master equation can be used for the…