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This study introduces an adaptive Trotterization algorithm for digital quantum simulation. It improves accuracy and manages errors in time-dependent quantum systems, outperforming fixed-step methods.

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Area of Science:

  • Quantum Information Science
  • Computational Physics
  • Quantum Computing

Background:

  • Digital quantum simulation uses Trotterization to approximate time evolution with quantum gates.
  • Current quantum processors face a trade-off between accuracy (finer time steps) and error rates (deeper circuits) due to gate imperfections.
  • Existing Trotterization methods struggle with time-dependent Hamiltonians and accumulating errors.

Purpose of the Study:

  • To develop an adaptive Trotterization algorithm for more accurate digital quantum simulations.
  • To address the limitations of fixed-step Trotterization in the presence of gate errors and time-dependent systems.
  • To provide a method for bounding accumulated errors in quantum simulations.

Main Methods:

  • Introduced an adaptive Trotterization algorithm for time-dependent Hamiltonians.
  • Proposed using piecewise "conserved" quantities to estimate time evolution errors.
  • Developed a scheme to bound errors over the full simulation period.
  • Validated the algorithm on a time-dependent quantum spin chain.

Main Results:

  • The adaptive algorithm effectively manages errors in time evolution.
  • Piecewise conserved quantities provide error bounds for the simulation.
  • The method reduces to standard conservation laws for time-independent Hamiltonians.
  • Demonstrated superior performance compared to conventional Trotter algorithms with fixed step sizes.

Conclusions:

  • The adaptive Trotterization algorithm offers improved accuracy and controlled errors for digital quantum simulations.
  • This approach is particularly beneficial for noisy intermediate-scale quantum (NISQ) devices.
  • The algorithm provides a robust method for simulating time-dependent quantum systems.