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Clifford Dressed Time-Dependent Variational Principle.

Antonio Francesco Mello1, Alessandro Santini1, Guglielmo Lami2

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|May 2, 2025
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Summary
This summary is machine-generated.

We developed a new quantum algorithm using Clifford disentangling techniques to better manage entanglement in simulations. This enhanced time-dependent variational principle (TDVP) method improves accuracy and efficiency for complex quantum systems.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Quantum Many-Body Systems

Background:

  • Matrix product states (MPS) are crucial for simulating quantum many-body systems.
  • Entanglement growth in MPS simulations poses significant computational challenges.
  • Standard time-dependent variational principle (TDVP) methods struggle with managing large entanglement.

Purpose of the Study:

  • To introduce an enhanced TDVP algorithm for efficient entanglement management in MPS.
  • To leverage Clifford group properties for reducing computational complexity.
  • To improve the accuracy and simulation time of quantum many-body system dynamics.

Main Methods:

  • Developed a Clifford dressed single-site 1-TDVP scheme.
  • Applied global Clifford transformations to reduce entanglement during TDVP integration.
  • Utilized checkerboard-patterned two-qubit Clifford unitaries for entanglement reduction.
  • Proposed incorporating Clifford gates within the two-site 2-TDVP scheme.

Main Results:

  • The Clifford dressed TDVP significantly improves entanglement management.
  • Achieved higher accuracy and extended simulation times compared to standard TDVP.
  • Demonstrated enhanced precision in computed observables for various quantum models.
  • Validated the algorithm's effectiveness on both integrable and nonintegrable systems.

Conclusions:

  • The proposed Clifford dressed TDVP offers a more efficient and accurate approach for simulating quantum many-body systems.
  • This method effectively mitigates the challenges associated with entanglement growth in MPS.
  • The integration of Clifford gates presents a promising direction for future quantum simulation algorithms.