Efficient Description of Many-Body Systems with Matrix Product Density Operators
Jiří Guth Jarkovský, András Molnár, Norbert Schuch, J. Ignacio Cirac
Abstract
Matrix product states form a powerful ansatz for the simulation of a wide range of one-dimensional quantum systems that are in a pure state. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law." However, in order to accurately capture the physics of realistic systems, one generally needs to apply a mixed-state description. In this work, we establish the mixed-state analog of this characterization. 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.
Topics & Concepts
AnsatzQuantum entanglementMatrix multiplicationProduct (mathematics)Density matrixMatrix (chemical analysis)MathematicsRange (aeronautics)Kronecker productStatistical physicsQuantumPower (physics)Quantum systemApplied mathematicsOrder (exchange)Matrix product stateQuantum computerPhysicsTopology (electrical circuits)Quantum mechanicsWork (physics)Computer scienceAlgebra over a fieldPure mathematicsSimple (philosophy)Operator (biology)Matrix algebraAlgorithmMatrix decompositionQuantum many-body systemsQuantum Computing Algorithms and ArchitectureQuantum Information and Cryptography