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Graphs disconnected by removing few vertices enable efficient quantum computation. Such networks allow universal quantum computation with minimal control, and estimating ground states is computationally feasible.

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Area of Science:

  • Quantum Information Science
  • Graph Theory
  • Computational Complexity

Background:

  • Quantum networks require efficient control for universal quantum computation.
  • Controllability of quantum systems is often limited by network topology.
  • Understanding graph properties is crucial for designing scalable quantum networks.

Purpose of the Study:

  • To investigate the relationship between graph properties and quantum network controllability.
  • To establish criteria for efficient quantum computation in complex networks.
  • To analyze the computational complexity of ground state estimation for Hamiltonians on controllable graphs.

Main Methods:

  • Analyzing graph connectivity and vertex removal properties.
  • Developing theoretical frameworks for quantum network control.
  • Applying graph theory to quantum systems and computational complexity.
  • Investigating finite-dimensional lattices, percolation clusters, and random graphs.

Main Results:

  • Networks with graphs disconnectable by minimal vertex removal are efficiently controllable.
  • Universal quantum computation is achievable with polynomial control sequences and minimal subsystem control.
  • Finite-dimensional lattices, percolation clusters, and random graphs exhibit efficient controllability.
  • Estimating ground states of Hamiltonians on controllable graphs has polynomial classical computational complexity.

Conclusions:

  • Graph structure significantly impacts quantum network efficiency and controllability.
  • Efficient quantum computation and ground state estimation are feasible in specific network architectures.
  • This research provides a foundation for designing scalable and controllable quantum systems.