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Augmenting Density Matrix Renormalization Group with Clifford Circuits.

Xiangjian Qian1, Jiale Huang1, Mingpu Qin1,2

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This summary is machine-generated.

We integrated Clifford circuits into the density matrix renormalization group (DMRG) algorithm to improve simulations of quantum many-body systems. This approach enhances accuracy for complex systems with minimal computational overhead.

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Area of Science:

  • Computational Physics
  • Quantum Many-Body Systems
  • Quantum Information Science

Background:

  • The density matrix renormalization group (DMRG) is a powerful method for one-dimensional quantum systems.
  • DMRG faces limitations in simulating two-dimensional systems due to the restricted entanglement in matrix product states.
  • Clifford circuits can simulate highly entangled stabilizer states but are limited in scope.

Purpose of the Study:

  • To develop a novel computational framework by integrating Clifford circuits with the DMRG algorithm.
  • To overcome the limitations of traditional DMRG in handling entanglement in higher dimensions.
  • To enhance the accuracy and applicability of quantum many-body simulations.

Main Methods:

  • Seamless integration of Clifford circuits within the existing DMRG algorithm.
  • Leveraging the strengths of both Clifford circuits (entanglement handling) and DMRG (accuracy in 1D).
  • Utilizing matrix product states as the wave-function Ansatz.

Main Results:

  • Achieved significant enhancements in simulation accuracy for quantum many-body systems.
  • Demonstrated that the integration introduces only a small additional computational cost.
  • The combined framework effectively handles states with substantial entanglement.

Conclusions:

  • The integration of Clifford circuits and DMRG offers a powerful new approach for simulating complex quantum systems.
  • This hybrid method significantly improves accuracy without a prohibitive increase in computational resources.
  • The framework is versatile and adaptable for various other numerical simulation techniques.