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Renormalized Circuit Complexity.

Arpan Bhattacharyya1,2, Pratik Nandy3, Aninda Sinha3

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This summary is machine-generated.

We optimized quantum circuit complexity for Hamiltonian simulation using the Suzuki-Trotter method. This novel approach enhances gate counting efficiency and reveals holographic connections in quantum systems.

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Area of Science:

  • Quantum Information Science
  • Theoretical Physics
  • Computational Complexity

Background:

  • Nielsen's circuit complexity is crucial for understanding quantum computation.
  • The Suzuki-Trotter (ST) method is a standard technique for approximating Hamiltonian dynamics.
  • Efficient quantum circuit design is essential for scalable quantum computing.

Purpose of the Study:

  • To modify Nielsen's circuit complexity for Hamiltonian simulation using the ST method.
  • To optimize gate counting in quantum circuits.
  • To explore holographic interpretations of quantum complexity.

Main Methods:

  • Modification of Nielsen's circuit complexity framework.
  • Application of the Suzuki-Trotter (ST) method for Hamiltonian simulation.
  • Analysis of gate density and its correlation with error tolerance.

Main Results:

  • A network-like structure for quantum circuits was established.
  • Optimized gate counting was achieved, scaling linearly with geodesic distance and spatial volume.
  • The ST iteration order was found to correlate with error tolerance, analogous to an anti-de Sitter radial coordinate.
  • Gate density was shown to be monotonically related to tolerance.
  • A holographic interpretation using path-integral optimization was provided.

Conclusions:

  • The proposed modification offers a more efficient approach to quantum circuit complexity for Hamiltonian simulation.
  • The findings suggest a deep connection between quantum error correction, circuit complexity, and holographic principles.
  • This work paves the way for more resource-efficient quantum algorithms and simulations.