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Fixed Depth Hamiltonian Simulation via Cartan Decomposition.

Efekan Kökcü1, Thomas Steckmann1, Yan Wang2

  • 1Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.

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Summary
This summary is machine-generated.

Optimizing quantum circuits for Hamiltonian simulations is crucial. Our new algorithm uses Cartan decomposition to create efficient, time-independent depth circuits, drastically improving simulation precision for various models.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Quantum Simulation

Background:

  • Simulating quantum dynamics on classical computers is memory-intensive for large systems.
  • Quantum computers offer a promising alternative, but circuit optimization is challenging.

Purpose of the Study:

  • To develop a constructive algorithm for optimizing quantum circuits for Hamiltonian simulations.
  • To generate quantum circuits with time-independent depth, minimizing quantum resources.

Main Methods:

  • The algorithm is based on Cartan decomposition of the Lie algebra generated by the Hamiltonian.
  • It is applied to special classes of models, including Anderson localization in a 1D transverse field XY model.

Main Results:

  • The algorithm generates quantum circuits with time-independent depth.
  • For the Anderson localization model, O(n^2)-gate circuits emerge.
  • The proposed method significantly improves simulation precision compared to product formulas.

Conclusions:

  • The algorithm provides exact circuits for diverse spin and fermionic models.
  • It offers analytic and numerical insights into optimal Hamiltonian simulations.