相关论文: Defining quantum divergences via convex optimizati…
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…
We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for…
For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…
This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are…
In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension $n$, are those linear maps that can be expressed as a convex combination of conjugations by $n\times n$ complex unitary matrices.…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
We investigate the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We…
Any reasonable measure of distinguishability of quantum states must satisfy a data processing inequality, that is, it must not increase under the action of a quantum channel. We can ask about the proportion of information lost or preserved…
The doubly minimized Petz Renyi mutual information of order $\alpha$ is defined as the minimization of the Petz divergence of order $\alpha$ of a fixed bipartite quantum state relative to any product state. The doubly minimized sandwiched…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all…
In Ref. [1], we proved a duality between two optimizations problems. The primary one is, given two quantum channels M and N, to find a quantum channel R such that RN is optimally close to M as measured by the worst-case entanglement…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
We address differential privacy for fully distributed optimization subject to a shared inequality constraint. By co-designing the distributed optimization mechanism and the differential-privacy noise injection mechanism, we propose the…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
The recently introduced random purification channel, which converts $n$ copies of an arbitrary mixed quantum state into $n$ copies of the same uniformly random purification, has emerged as a powerful tool in quantum information theory.…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the…