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Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …
A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps
M Idel - arxiv preprint arxiv:1609.06349, 2016 - arxiv.org
Given a nonnegative matrix $ A $, can you find diagonal matrices $ D_1,~ D_2 $ such that $
D_1AD_2 $ is doubly stochastic? The answer to this question is known as Sinkhorn's …
D_1AD_2 $ is doubly stochastic? The answer to this question is known as Sinkhorn's …
Preparation of matrix product states with log-depth quantum circuits
We consider the preparation of matrix product states (MPS) on quantum devices via
quantum circuits of local gates. We first prove that faithfully preparing translation-invariant …
quantum circuits of local gates. We first prove that faithfully preparing translation-invariant …
Constant-depth preparation of matrix product states with adaptive quantum circuits
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and
feedforward operations, have recently emerged as a promising avenue for efficient state …
feedforward operations, have recently emerged as a promising avenue for efficient state …
Classifying quantum phases using matrix product states and projected entangled pair states
We give a classification of gapped quantum phases of one-dimensional systems in the
framework of matrix product states (MPS) and their associated parent Hamiltonians, for …
framework of matrix product states (MPS) and their associated parent Hamiltonians, for …
Tensor network formulation of symmetry protected topological phases in mixed states
We define and classify symmetry-protected topological (SPT) phases in mixed states based
on the tensor network formulation of the density matrix. In one dimension, we introduce …
on the tensor network formulation of the density matrix. In one dimension, we introduce …
Quantum metropolis sampling
The original motivation to build a quantum computer came from Feynman, who imagined a
machine capable of simulating generic quantum mechanical systems—a task that is …
machine capable of simulating generic quantum mechanical systems—a task that is …
Randomized benchmarking with confidence
Randomized benchmarking is a promising tool for characterizing the noise in experimental
implementations of quantum systems. In this paper, we prove that the estimates produced by …
implementations of quantum systems. In this paper, we prove that the estimates produced by …
Exact dynamics in dual-unitary quantum circuits
We consider the class of dual-unitary quantum circuits in 1+ 1 dimensions and introduce a
notion of “solvable” matrix product states (MPSs), defined by a specific condition which …
notion of “solvable” matrix product states (MPSs), defined by a specific condition which …
Quantum reservoir computing in finite dimensions
Most existing results in the analysis of quantum reservoir computing (QRC) systems with
classical inputs have been obtained using the density matrix formalism. This paper shows …
classical inputs have been obtained using the density matrix formalism. This paper shows …