Related papers: Structure and Classification of Matrix Product Qua…
A class of quantum channels and completely positive maps (CPMs) are introduced and investigated. These, which we call subspace preserving (SP) CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve…
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly…
Hybrid quantum-classical models offer a promising route for learning from complex data; however, their application to multi-band remote sensing imagery often relies on generic, data-agnostic quantum circuits that fail to account for…
We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite…
Many alternative approaches to construct quantum channels with large entangling capacity were proposed in the past decade, resulting in multiple isolated gates. In this work, we put forward a novel one, inspired by convolution, which…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
Variational Quantum Circuits (VQC) are promising models for quantum machine learning, but standard monolithic architectures face an expressivity--trainability dilemma: small circuits can be under-parameterized, while larger circuits are…
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground…
If $H_1$ and $H_2$ are finite-dimensional Hilbert spaces, a channel from $H_1$ to $H_2$ is a completely positive, linear map $\mathcal{I}$ that takes the set of states $\mathcal{S}(H_1)$ for $H_1$ to the set of states $\mathcal{S}(H_2)$ for…
Measurement-based quantum computation (MBQC) is a model of quantum computation, in which computation proceeds via adaptive single qubit measurements on a multi-qubit quantum state. It is computationally equivalent to the circuit model.…
Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a…
The quantum process framework is devised as a generalization of quantum theory to incorporate indefinite causal structure. In this short paper we point out a restriction in forming products of processes: there exist both classical and…
Quantum networks, which integrate multiple quantum computers and the channels connecting them, are crucial for distributed quantum information processing but remain inherently susceptible to channel noise. Channel purification emerges as a…
Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC). This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes by…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous…
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
We have developed a new approach based on matrix product representations of ground states to study Quantum Phase Transitions (QPT). As confirmation of the power of our approach we have analytically analyzed the XXZ spin-one chain with…