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Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

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This study demonstrates universal adiabatic quantum computation using local interactions on a 2D grid. The research bounds the eigenvalue gap, connecting it to quantum walks on Young

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Adiabatic quantum computation (AQC) offers a potential pathway for quantum computation.
  • Implementing universal AQC requires complex Hamiltonians and precise control.
  • Understanding the energy gap is crucial for AQC performance and error rates.

Purpose of the Study:

  • To present a novel Hamiltonian for universal adiabatic quantum computation.
  • To analyze the eigenvalue gap of the proposed Hamiltonian.
  • To establish connections between AQC and other quantum mechanical models.

Main Methods:

  • Utilizing a Hamiltonian with local interactions on a two-dimensional grid.
  • Adiabatically changing a single parameter in the Hamiltonian to simulate quantum circuits.
  • Mapping the model to the ferromagnetic XXZ chain with kink boundary conditions.
  • Leveraging exact solutions for the spin chain gap using SU(2) symmetry.

Main Results:

  • Demonstrated a method for universal adiabatic quantum computation.
  • Bounded the eigenvalue gap above the unique ground state.
  • Established an equivalence between the time evolution and quantum walks on Young's lattice for large system sizes.
  • Discussed a related time-independent Hamiltonian for universal computation.

Conclusions:

  • The proposed model provides a viable framework for universal adiabatic quantum computation.
  • The analysis of the eigenvalue gap offers insights into the computational feasibility and robustness of the system.
  • The connection to quantum walks highlights potential interdisciplinary applications and theoretical links.