Entanglement entropy and the simulation of Quantum Mechanics

Abstract

The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum systems. Further applications of the techniques based on matrix product states, some of their spin-off and their recent generalizations to scale invariant theories and higher dimensions systems are also discussed.

9 pages. Contribution to the Proceedings of the IRGAC conference held at Barcelona, July 2006

References in corpus (9)

• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• An entanglement-area law for general bosonic harmonic lattice systems
• Renormalization group transformations on quantum states
• Fine-grained entanglement loss along renormalization group flows
• Simulation of many-qubit quantum computation with matrix product states

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• Holographic Entanglement Entropy: An Overview
• Entanglement Entropy from a Holographic Viewpoint
• A short review on entanglement in quantum spin systems
• Supersonic quantum communication
• Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
• Particle entanglement in continuum many-body systems via quantum Monte Carlo
• A variational method based on weighted graph states
• Rényi Entropy of Free Compact Boson on Torus
• Non-Markovian Quantum Dynamics and Classical Chaos
• The Prime state and its quantum relatives
• Entanglement in Theory Space