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

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.