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Clifford Circuits Augmented Time-Dependent Variational Principle.

Xiangjian Qian1, Jiale Huang1, Mingpu Qin1,2

  • 1Shanghai Jiao Tong University, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai 200240, China.

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

We introduce a new method combining Clifford circuits with the time-dependent variational principle (TDVP) to simulate many-body quantum systems. This approach reduces entanglement, enabling more reliable and longer-term simulations with fewer computational resources.

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Area of Science:

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

Background:

  • Matrix Product States (MPS) are powerful for simulating quantum systems.
  • Density Matrix Renormalization Group (DMRG) is a common MPS-based algorithm.
  • Simulating time evolution in quantum systems is computationally demanding due to entanglement growth.

Purpose of the Study:

  • To generalize Clifford Circuits Augmented Matrix Product States (CA-MPSs) to time evolution simulations.
  • To develop a computationally efficient method for simulating the dynamics of many-body quantum systems.
  • To reduce entanglement entropy during time evolution for improved simulation accuracy and duration.

Main Methods:

  • The study generalizes CA-MPSs to the Time-Dependent Variational Principle (TDVP) framework.
  • Clifford circuits are applied in each TDVP step with a two-site sweeping process to reduce entanglement entropy.
  • The Hamiltonian is transformed using Clifford circuits, with minimal overhead as the number of terms does not increase.

Main Results:

  • The Clifford Circuits Augmented TDVP method successfully reduces entanglement entropy during time evolution.
  • Simulations in XXZ and 2D Heisenberg models, and the Kitaev honeycomb model show improved reliability over longer time scales.
  • The method demonstrates the ability to handle non-stabilizer entanglement efficiently.

Conclusions:

  • The Clifford Circuits Augmented TDVP method is a valuable tool for simulating the time evolution of many-body quantum systems.
  • This approach offers a significant reduction in computational resources required for accurate simulations.
  • The method enhances the reliability and duration of quantum system time evolution simulations.