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A class of quantum many-body states that can be efficiently simulated

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arxiv quant-ph/0610099 v1 pith:O3OMKJEH submitted 2006-10-12 quant-ph cond-mat.str-el

G. Vidal This is my paper · ORCID
classification quant-phcond-mat.str-el
keywords quantumentanglementlatticemany-bodymerarenormalizationstatesstructure
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We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.

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Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Renormalization flows for 1D mixed states and a quantum Goursat lemma

    math-ph 2026-07 accept novelty 7.5 of 10

    Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.

  2. Two-dimensional Hyperbolic RNN Neural Quantum State

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    Lorentz 2DRNN introduces the first 2D hyperbolic NQS and outperforms Euclidean 2DRNN at the 2DTFIM critical point; 1D hyperbolic NQS also tested on reshaped 2D lattices.

  3. Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Twirled perfect tensor networks are introduced as a class satisfying computational covariance, bounding complexity by the Python's Lunch Conjecture exponent, and combining holographic features of perfect and random te...

  4. Symmetry-Resolved Entanglement Entropy from Heat Kernels

    hep-th 2025-11 unverdicted novelty 7.0 of 10

    An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.

  5. A Unitary Encoder for Surface Codes

    quant-ph 2025-06 conditional novelty 7.0 of 10

    A new non-local unitary encoder grows a rotated surface code from distance d to 2d-1 in four time steps, giving about 43% less depth than the previous best logarithmic-depth encoder.

  6. QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

    hep-th 2024-12 conditional novelty 7.0 of 10

    A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.

  7. Shallow Unitary Circuits for Kramers-Wannier Dualities

    quant-ph 2026-07 unverdicted novelty 6.0 of 10

    Log-depth nonlocal unitary circuits realize exact Z2 and Zn KW dualities that map arbitrary SRE states to LRE duals in the symmetric sector.

  8. CFT Complexity and Penalty Factors

    hep-th 2025-07 conditional novelty 6.0 of 10

    A submersion-based method turns weighted generator costs into state-complexity metrics for CFTs, giving analytic formulas in simple limits and constraints on which weight choices are viable.

  9. Celestial Quantum Error Correction II: From Qudits to Celestial CFT

    hep-th 2024-12 conditional novelty 6.0 of 10

    A GKP-style qudit code on a chain embedded in Klein spacetime is shown to flow, in the continuum limit, to a celestial CFT whose logical states carry quantized supertranslation hair protected from soft graviton errors.

  10. The thread embodiment of holographic quantum entanglement

    hep-th 2025-01 conditional novelty 5.0 of 10

    Holographic entanglement is represented by geodesic threads whose fluxes equal half conditional mutual information, and kinematic space is treated as the input board of a quantum circuit that reproduces holographic co...

  11. Mapping the Hubbard model to the t-J model using ground state unitary transformations

    cond-mat.str-el 2019-08 conditional novelty 5.0 of 10

    A tensor-network optimized unitary transforms the Hubbard model into Heisenberg and t-J effective models, confirming the half-filling result J = 4t^2/U but with poor accuracy for doped systems.

  12. TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models

    physics.comp-ph 2019-06 unverdicted novelty 4.0 of 10

    TensorFlow-backed TensorNetwork implementation of MERA for critical 1D Ising model with conformal data extraction and 200x GPU acceleration reported.

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