An Approach for Distributed Quantum Simulation of Fermionic Systems

Simulating fermionic systems on near-term quantum computers is constrained by severe qubit limitations, motivating the exploration of distributed quantum computing architectures. Circuit knitting offers a promising approach to partition large quantum circuits across multiple quantum processing units, but naive implementations incur exponential classical overhead. We introduce a framework for characterizing what we call incompatibility between components in fermionic Hamiltonians. For example, certain decomposition structures enable efficient circuit partitioning by identifying regions of minimal entanglement, reducing classical post-processing from exponential to a manageable bounded cost. We demonstrate this framework on benchmark fermionic systems and analyze the scaling of decomposition properties with system size. Preliminary results suggest that real fermionic Hamiltonians may naturally exhibit favorable structural patterns amenable to distributed simulation. This work provides both theoretical understanding and practical guidance for identifying systems suitable for efficient circuit knitting on distributed quantum-classical HPC platforms.