Computational complexity of injective projected entangled pair states

• URL: http://arxiv.org/abs/2509.19963v1
• Date: Wed, 24 Sep 2025 10:17:23 GMT
• Title: Computational complexity of injective projected entangled pair states
• Authors: Dylan Harley, Freek Witteveen, Daniel Malz,
• Abstract summary: Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement.<n> PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians.<n>Injective PEPS, where all constituent tensors fulfil an injectivity constraint, are generally believed to be better behaved.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement. PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians. However, computing local expectation values in these states is known to be postBQP-hard. Injective PEPS, where all constituent tensors fulfil an injectivity constraint, are generally believed to be better behaved, because they are unique ground states of spatially local Hamiltonians. In this work, we therefore examine how the computational hardness of contraction depends on the injectivity. We establish that below a constant positive injectivity threshold, evaluating local observables remains postBQP-complete, while above a different constant nontrivial threshold there exists an efficient classical algorithm for the task. This resolves an open question from (Anshu et al., STOC `24).

Related papers

• Entanglement generation in qubit-ADAPT-VQE through four-qubit algebraic classification [0.0]
  ADAPT-VQE has been extensively benchmarked on molecular Hamiltonians, where the ground states typically exhibit low entanglement.<n>We explore a variant of this algorithm known as qubit-ADAPT-VQE, assessing its ability to achieve ground states with substantial entanglement in spin models.<n>Our findings highlight the versatility of qubit-ADAPT-VQE, demonstrating that it accurately reaches the ground state across all entanglement classes and initial energy values.
  arXiv  Detail & Related papers  (2025-12-12T17:10:51Z)
• Extracting conserved operators from a projected entangled pair state [5.607590231264275]
  Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate?<n>We show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians.<n>In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state.
  arXiv  Detail & Related papers  (2025-11-25T18:43:47Z)
• Physically-Motivated Guiding States for Local Hamiltonians [0.0]
  We focus on states motivated by Quantum Chemistry and Hamiltonian subset states.<n>We demonstrate that broader state families preserve hardness, while maintaining classical tractability.<n>Our work furthers the landscape complexity for ground state estimation problems, presenting steps toward experimentally relevant settings.
  arXiv  Detail & Related papers  (2025-09-30T05:47:13Z)
• Gaussian fermionic embezzlement of entanglement [41.321581612257056]
  We show that the embezzling property is in fact a generic property of fermionic Gaussian states.<n>We bridge finite-size systems to abstract characterizations based on the classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2025-09-19T08:26:03Z)
• Quantum Gibbs states are locally Markovian [1.9643748953805944]
  We show that for any Hamiltonian with a bounded interaction degree, the quantum Gibbs state is locally Markov at arbitrary temperature.<n>We introduce a regularization scheme for imaginary-time-evolved operators at arbitrarily low temperatures.
  arXiv  Detail & Related papers  (2025-04-03T01:54:42Z)
• Nonlocality under Jaynes-Cummings evolution: beyond pseudospin operators [44.99833362998488]
  We re-visit the generation and evolution of (Bell) nonlocality in hybrid scenarios whose dynamics is determined by the Jaynes-Cummings Hamiltonian. Recent results on the optimal Bell violation in qubit-qudit systems show that the nonlocality is much greater than previously estimated.
  arXiv  Detail & Related papers  (2024-10-14T16:01:23Z)
• Dynamical localization in 2D topological quantum random walks [0.0]
  We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect.<n>By investigating the spectral properties of the discrete-time evolution operators, we show that trapped states have large overlap with the initial uniformly distributed state.<n>We show that mechanism of localization we identified is robust against the influence of disorder.
  arXiv  Detail & Related papers  (2024-06-26T21:36:47Z)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Efficient Verification of Ground States of Frustration-Free Hamiltonians [28.03059224016627]
  We propose a recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. We derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma and quantum union bound. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.
  arXiv  Detail & Related papers  (2022-06-30T13:50:56Z)
• Universality-of-clock-rates test using atom interferometry with $T^{3}$ scaling [63.08516384181491]
  Atomic clocks generate delocalized quantum clocks. Tests of universality of clock rates (one facet of LPI) to atom interferometry generating delocalized quantum clocks proposed. Results extend our notion of time, detached from classical and localized philosophies.
  arXiv  Detail & Related papers  (2022-04-05T12:26:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.