Entropy scaling and simulability by matrix product states.

By Norbert Schuch, Michael M. Wolf, Frank Verstraete, J. I. Cirac. Physical Review Letters, 2007

340 citations recorded by the source corpus.

We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Rényi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f48b41dceca59412eca55477d55d2469f1134a65

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. A. Nahum
2. Pasquale Calabrese
3. J. Dubail
4. V. Khemani
5. Andrew J. Daley
6. J. Cardy
7. M. Fagotti
8. Matthew Fisher

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Pasquale Calabrese
3. J. Dubail
4. V. Khemani
5. Andrew J. Daley
6. J. Cardy
7. Matthew Fisher
8. M. Fagotti

In Statistical and Nonlinear Physics

1. Andrew J. Daley
2. Pasquale Calabrese
3. J. Dubail
4. A. Nahum
5. J. Cardy
6. V. Khemani
7. Frank Pollmann
8. M. Fagotti

Citations in the corpus

• Hand-waving and interpretive dance: an introductory course on tensor networks (2016, background): “Tensor network states therefore provide an important analytic framework for understanding the universal properties of classes of states which possess particular properties, such as those which only support certain entanglement or correlation structures.”
• Random Quantum Circuits (2022, background): “A generalization of this idea to Matrix Product States (MPS) for 1D chains means that there is a direct relation between the entanglement of a 1D quantum state and the cost of storing it as an MPS (86).”
• Unusual corrections to scaling in entanglement entropy (2010, background): “t the entanglement than the widely studied von Neumann entropy S(1) A . It also gives a fundamental insight into understanding the convergence and scaling of algorithms based on matrix product states [3]. In [4, 5, 6] it was shown that for a one-dimensional critical system whose scaling limit is des”
• Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “Conversely, it holds that a state with an entanglement entropy satisfying a volume law for the von Neumann entropy cannot be approximated faithfully using MPS, but this problem is undetermined for the α < 1 Renyi entropies (Schuch et al., 2008c). b.”
• Entanglement and correlation functions following a local quench: a conformal field theory approach (2007, neutral): “Comparison with numerical works . . . . . . . . . . . . . . . . . . . . . . . 12”
• Time-evolution methods for matrix-product states (2019, methodology): “Nowadays, DMRG methods formulated in the language of matrix-product states[9–14] (MPS) are the de facto standard for the investigation of one-dimensional systems.”
• Quantum trajectories and open many-body quantum systems (2014, methodology): “In the generic case [248, 249, 257], this leads to a linear growth in the entanglement entropy as a function of time.”
• Measuring entanglement entropy in a quantum many-body system (2015, background): “Entanglement entropy can be used to probe quantum criticality [19] and non-equilibrium dynamics [20, 21], and to determine whether efficient numerical techniques for computing many-body physics exist [22].”
• Entanglement entropy of two disjoint blocks in XY chains (2010, background): “It also gives a fundamental insight into understanding the convergence and scaling of algorithms based on matrix product states [3].”