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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

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Published on: May 30, 2014

Preparing projected entangled pair states on a quantum computer.

Martin Schwarz1, Kristan Temme, Frank Verstraete

  • 1Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Vienna, Austria.

Physical Review Letters
|May 1, 2012
PubMed
Summary
This summary is machine-generated.

We developed a quantum algorithm for preparing projected entangled pair states (PEPS), a type of quantum state representation. This algorithm offers polynomial runtime scaling related to PEPS properties and Hamiltonian spectral gaps.

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Area of Science:

  • Quantum computing
  • Quantum information theory
  • Condensed matter physics

Background:

  • Projected entangled pair states (PEPS) are a powerful class of tensor networks used to represent complex quantum states.
  • Efficiently preparing and simulating PEPS on quantum computers is crucial for advancing quantum many-body physics.

Purpose of the Study:

  • To introduce a novel quantum algorithm for the preparation of injective projected entangled pair states (PEPS).
  • To analyze the computational complexity and scaling of the proposed quantum algorithm.

Main Methods:

  • Development of a quantum algorithm specifically designed for PEPS preparation.
  • Analysis of the algorithm's runtime complexity based on the condition number of PEPS projectors.
  • Investigation of the relationship between runtime and the spectral gap of the PEPS's parent Hamiltonian.

Main Results:

  • The algorithm successfully prepares injective PEPS on a quantum computer.
  • Runtime complexity scales polynomially with the inverse of the minimum condition number of PEPS projectors.
  • Runtime also scales polynomially with the inverse of the spectral gap of the PEPS's parent Hamiltonian.

Conclusions:

  • The presented quantum algorithm provides an efficient method for preparing injective PEPS.
  • The findings offer insights into the resource requirements for simulating quantum states using PEPS on quantum hardware.
  • This work contributes to the development of quantum algorithms for studying complex quantum systems.