Related papers: Structure and Classification of Matrix Product Qua…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
This paper presents QCommE2E as an open-source simulation framework for end-to-end quantum communication systems, with explicit tutorial emphasis. The primary objective is to develop a comprehensive framework that includes transmitters,…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
This work investigates the application of quantum machine learning techniques for classical and quantum communication across different qubit channel models. By employing parameterized quantum circuits and a flexible channel noise model, we…
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in…
Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…
Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace…
Transformers process tokens in parallel but are temporally shallow: at position $t$, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer…
We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using…
We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing…
Transformers are deep architectures that define "in-context mappings" which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In this work, we…
We present a coherent approach to recurrence and transience, starting from a version of the Riesz decomposition theorem for superharmonic elements. Our approach allows straightforward proofs of some known results, entails new theorems, and…
Are multi-layer parameterized quantum circuits (MPQCs) more expressive than classical neural networks (NNs)? How, why, and in what aspects? In this work, we survey and develop intuitive insights into the expressive power of MPQCs in…
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination,…
While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics such as topological phases of matter. Furthermore, mounting evidence originating from…
Quantum machine learning (QML) leverages quantum computing for classical inference, furnishes the processing of quantum data with machine-learning methods, and provides quantum algorithms adapted to noisy devices. Typically, QML proposals…
We study whether one can write a Matrix Product Density Operator (MPDO) as the Gibbs state of a quasi-local parent Hamiltonian. We conjecture this is the case for generic MPDO and give supporting evidences. To investigate the locality of…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
In a recent paper, Hirche and Leditzky introduced the notion of bi-PPT channels which are quantum channels that stay completely positive under composition with a transposition and such that the same property holds for one of their…
We develop a new projected wave function approach which is based on projection operators in the form of matrix-product operators (MPOs). Our approach allows to variationally improve the short range entanglement of a given trial wave…