Efficient description of many-body systems with Matrix Product Density Operators

Abstract

Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In this work, we establish the mixed state analogue of this result: We show that one-dimensional mixed states with a low amount of entanglement, quantified by the entanglement of purification, can be efficiently approximated by Matrix Product Density Operators (MPDOs). In combination with results establishing area laws for thermal states, this helps to put the use of MPDOs in the simulation of thermal states on a formal footing.

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Cited by in corpus (31)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Entanglement Barriers in Dual-Unitary Circuits
• Classical simulation of lossy boson sampling using matrix product operators
• Simulating Noisy Quantum Circuits with Matrix Product Density Operators
• Computable Rényi mutual information: Area laws and correlations
• Holographic simulation of correlated electrons on a trapped ion quantum processor
• Comparing bipartite entropy growth in open-system matrix-product simulation methods
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Quantum State Tomography for Matrix Product Density Operators
• Quantifying Non-Markovianity in Open Quantum Dynamics
• Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects
• Decay of quantum conditional mutual information for purely generated finitely correlated states
• Rényi free energy and variational approximations to thermal states
• Reconstructing Non-Markovian Open Quantum Evolution From Multi-time Measurements
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• Quantum Tensor Product Decomposition from Choi State Tomography
• Thermal Area Law for Lattice Bosons
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Matrix product states and the decay of quantum conditional mutual information
• Prolonging a discrete time crystal by quantum-classical feedback
• Variational Neural and Tensor Network Approximations of Thermal States
• Locally accurate matrix product approximation to thermal states
• Non-unitarity maximizing unraveling of open quantum dynamics
• On the connection between least squares, regularization, and classical shadows
• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
• Approximate tensor decompositions: disappearance of many separations
• Measurement-induced entanglement in noisy 2D random circuits
• Learning mixed quantum states in large-scale experiments
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings