Clifford Circuit-Based Heuristic Optimization of Fermion-To-Qubit Mappings.

Area of Science:

• Quantum computing
• Computational physics
• Quantum information science

Background:

• Simulating interacting Fermionic Hamiltonians is a key application for quantum computers.
• Efficient Fermion-to-qubit mappings are crucial for encoding nonlocal Fermionic degrees of freedom into local qubit degrees of freedom.
• Existing mapping methods are often restricted or rely on computationally expensive brute-force searches.

Purpose of the Study:

• To develop a scalable and effective heuristic numerical optimization framework for Fermion-to-qubit mappings.
• To design mappings tailored to specific quantum simulation Hamiltonians.
• To improve the efficiency of quantum simulations of Fermionic systems.

Main Methods:

• Translated the Fermion-to-qubit mapping problem into a Clifford circuit optimization problem.
• Employed simulated annealing to optimize the average Pauli weight of the problem Hamiltonian.
• Compared numerically optimized mappings against conventional methods, including ternary-tree-based mappings.

Main Results:

• Numerically optimized mappings consistently outperformed conventional counterparts across various Fermionic Hamiltonians.
• Achieved 15%-40% improvements in average Pauli weight for Hamiltonians of intermediate complexity.
• Demonstrated significant improvements for 6x6 nearest-neighbor hopping (>40%) and Hubbard models (>20%).
• Identified specific interaction Hamiltonians where optimized mappings surpassed all ternary-tree-based methods.

Conclusions:

• Heuristic numerical optimization provides an effective approach for generating tailored Fermion-to-qubit mappings.
• The developed framework enhances the feasibility and efficiency of quantum simulations for complex Fermionic systems.
• Optimized mappings represent a significant advancement in leveraging quantum computers for condensed matter physics and quantum chemistry.