Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science.

Area of Science:

• Quantum physics
• Computational condensed matter physics

Background:

• The Heisenberg model is a fundamental model in quantum magnetism.
• Simulating strongly correlated quantum systems, especially those with non-sparse ground states, presents significant computational challenges.
• The Sample-based Krylov Quantum Diagonalization (SKQD) algorithm is a novel approach for quantum system analysis.

Purpose of the Study:

• To evaluate the performance and accuracy of the SKQD algorithm on one- and two-dimensional Heisenberg models.
• To investigate SKQD's effectiveness in strongly correlated regimes with dense ground states.
• To assess SKQD's applicability on quantum hardware.

Main Methods:

• Application of the SKQD algorithm to Heisenberg models of varying dimensions.
• Utilizing problem-informed initial states and magnetization sector sweeps.
• Benchmarking SKQD results against Density Matrix Renormalization Group (DMRG) and exact diagonalization.
• Implementation and testing of SKQD on actual quantum hardware (qubits).

Main Results:

• SKQD accurately reproduces ground-state energies and field-dependent magnetization for Heisenberg models across different anisotropies.
• Qualitative agreement was observed when compared to established methods like DMRG.
• Accuracy of SKQD improves with increasing system anisotropy.
• Successful demonstration of SKQD on 18- and 30-qubit quantum processors, yielding expected magnetization curves.
• Effectiveness of SKQD extends to two-dimensional lattice systems, as indicated by simulations on a 64-qubit processor.

Conclusions:

• The SKQD algorithm is a robust and effective method for studying quantum magnetism, particularly for Heisenberg models.
• SKQD demonstrates reliable performance even for challenging problems with non-sparse ground states.
• The algorithm shows scalability and applicability to both one- and two-dimensional quantum systems, including on current quantum hardware.