Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

JI Cirac, D Perez-Garcia, N Schuch, F Verstraete - Reviews of Modern Physics, 2021‏ - APS
The theory of entanglement provides a fundamentally new language for describing
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 …

Preparation of matrix product states with log-depth quantum circuits

D Malz, G Styliaris, ZY Wei, JI Cirac - Physical Review Letters, 2024‏ - APS
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 …

Constant-depth preparation of matrix product states with adaptive quantum circuits

KC Smith, A Khan, BK Clark, SM Girvin, TC Wei - PRX Quantum, 2024‏ - APS
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and
feedforward operations, have recently emerged as a promising avenue for efficient state …

Classifying quantum phases using matrix product states and projected entangled pair states

N Schuch, D Pérez-García, I Cirac - Physical Review B—Condensed Matter …, 2011‏ - APS
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 …

Tensor network formulation of symmetry protected topological phases in mixed states

H Xue, JY Lee, Y Bao - arxiv preprint arxiv:2403.17069, 2024‏ - arxiv.org
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 …

Quantum metropolis sampling

K Temme, TJ Osborne, KG Vollbrecht, D Poulin… - Nature, 2011‏ - nature.com
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 …

Randomized benchmarking with confidence

JJ Wallman, ST Flammia - New Journal of Physics, 2014‏ - iopscience.iop.org
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 …

Exact dynamics in dual-unitary quantum circuits

L Piroli, B Bertini, JI Cirac, T Prosen - Physical Review B, 2020‏ - APS
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 …

Quantum reservoir computing in finite dimensions

R Martínez-Peña, JP Ortega - Physical Review E, 2023‏ - APS
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 …