Mapping of fermionic lattice models for Ising solvers.

Area of Science:

• Quantum Computing
• Computational Physics
• Materials Science

Background:

• Simulating quantum systems, such as interacting fermions and quantum spins, is computationally challenging.
• Current quantum annealers require specific problem formulations like Quadratic Unconstrained Binary Optimization (QUBO).
• Preserving the low-energy physics of quantum models during conversion is crucial for accurate results.

Purpose of the Study:

• To present an end-to-end, symmetry-aware pipeline for converting quantum models to annealer-ready QUBOs.
• To ensure the preservation of low-energy physics throughout the conversion process.
• To validate the pipeline's effectiveness across a range of quantum models and system sizes.

Main Methods:

• The pipeline integrates Bravyi-Kitaev encoding, exact symmetry tapering, Xia-Bian-Kais (XBK) diagonalization, and local quadratization.
• Ground state energies are recovered using a Dinkelbach fixed-point method on the Ising objective.
• Experiments utilize D-Wave's Advantage QPU and simulators, alongside exact diagonalization for validation.

Main Results:

• The pipeline successfully reproduced known physical transitions for a 2D Ising model.
• Simulations of 1D XXZ spin chains and interacting fermions (t-V model) matched exact diagonalization results.
• A study on replication factors quantified accuracy-overhead trade-offs, showing significant error reduction.

Conclusions:

• The developed pipeline offers a practical pathway for mapping quantum matter Hamiltonians to current quantum annealers.
• The approach allows for adjustable trade-offs between accuracy, computational resources, and embedding complexity.
• This work facilitates the use of quantum annealers for studying complex quantum phenomena.