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Xie-Hang Yu1, J Ignacio Cirac1, Pavel Kos1

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We introduce a new class of projected entangled pair states (PEPS) that efficiently characterizes complex quantum states. This advancement enables tractable calculations for observables and correlations, enhancing quantum many-body physics research.

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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Characterizing higher-dimensional many-body quantum states is computationally challenging.
  • Existing projected entangled pair states (PEPS) have limitations in calculating local observables and correlations.
  • Single isometric constraints in PEPS restrict analytical tractability for complex physical systems.

Purpose of the Study:

  • To propose a novel class of projected entangled pair states (PEPS) with enhanced computational capabilities.
  • To overcome the intractability of calculating general local observables and two-point correlation functions in many-body systems.
  • To explore the potential of this new PEPS class for representing quantum computation and topological order transitions.

Main Methods:

  • Introduction of a new PEPS formulation incorporating two isometric conditions.
  • Analytical derivation of methods for efficient calculation of local observables.
  • Demonstration of efficient calculation for specific two-point correlation functions.
  • Analysis of the parameter space and its relation to general PEPS.
  • Theoretical investigation into the capacity for universal quantum computation and topological order representation.

Main Results:

  • The proposed PEPS class allows efficient calculation of general local observables, previously intractable.
  • Certain two-point correlation functions become efficiently computable, a significant improvement over existing methods.
  • The new PEPS maintains rich physical structure while enhancing analytical tractability.
  • The class possesses a large set of tunable parameters with only a subleading correction to general PEPS.
  • Analytical proofs confirm the ability of this PEPS class to encode universal quantum computation.

Conclusions:

  • The novel, doubly isometrically constrained PEPS offers a powerful tool for characterizing complex quantum states.
  • This advancement significantly expands the scope of analytical and computational studies in quantum many-body physics.
  • The demonstrated capability to represent universal quantum computation and topological transitions highlights its broad applicability.