Class of quantum many-body states that can be efficiently simulated.

By Guifré Vidal. Physical Review Letters, 2006

778 citations recorded by the source corpus.

We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that the expectation value of local observables can be computed exactly and efficiently. The multiscale entanglement renormalization ansatz is equivalent to a quantum circuit of logarithmic depth that has a very characteristic causal structure. It is also the ansatz underlying entanglement renormalization, a novel coarse-graining scheme for many-body quantum systems on a lattice.

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

View Paper: https://www.semanticscholar.org/paper/9b56dd2fff7fd0c830ded3d156971a240f7f9334

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. D. Harlow
2. R. Myers
3. Sahel Ashhab
4. Shira Chapman
5. H. Marrochio
6. I. Georgescu
7. B. Yoshida
8. T. Takayanagi

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. B. Yoshida
5. Shira Chapman
6. H. Marrochio
7. R. Verresen
8. Sahel Ashhab

Citations in the corpus

• Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, methodology): “Tensor networks with open legs in the bulk were first proposed by Vidal [17].”
• Integral geometry and holography (2015, neutral): “in [45, 46].”
• Hierarchical quantum classifiers (2018, methodology): “In a conventional MERA network, the addition of these unitaries allows quantum correlations on a particular length scale to be captured at the same layer of the network.(10) A circuit diagram of an eightqubit MERA is shown in Fig.”
• Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification (2021, neutral): “[9] And for the input, we let each pixel of the input image as the bottom tensors.”
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, result): “In this case, λ depends on the number of layers of the MERA tensor network.”
• Quantum trajectories and open many-body quantum systems (2014, background): “Generalisations have been proposed to higher dimensions [240, 241], although these are typically very computationally intensive.”
• Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “An equally exciting question is whether our topological invariants can be efficiently detected in a tensor-network representation of the ground state, such as the multi-scale entanglement renormalization group ansatz (MERA) [129].”
• Why Does Deep and Cheap Learning Work So Well? (2016, background): “From this perspective, MERA is as an unsupervised machine learning algorithm, where classical probability distributions over many variables are replaced with quantum wavefunctions.”
• Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, methodology): “Our observation that the bipartite mutual information grows only logarithmically in time for completely-mixed initial states may aid numerical studies of the transition in nonstabilizer circuit models in 1D using matrix product methods, such as the multiscale entanglement renormalization ansatz (MER”
• Neural Network Renormalization Group (2018, background): “In particular, stacking bijectors to form a reversible transformation is analogous to the quantum circuit interpretation of MERA.”