Simulating computationally hard fermionic systems is a promising application of quantum computing. However, mapping nonlocal fermionic operators to qubits often produces deep circuits, rendering such simulations impractical on near-term hardware. We introduce two Majorana swap network compilation strategies for variational quantum eigensolvers that reduce circuit depth and two-qubit gate count. First, we develop a cyclic compilation algorithm that localizes all two-particle interaction terms in a general fermionic Hamiltonian containing up to $O\left(M^4\right)$ such terms using only $O\left(M^3\right)$ auxiliary Majorana-swap transpositions, where $M$ is the number of fermionic modes. Here, the cubic scaling refers to auxiliary routing; a complete UCCGSD Ansatz still contains $O\left(M^4\right)$ double-excitation rotations. Second, we design a Majorana-swap network for the $k$-UpCCGSD variational Ansatz, which is already more compact than UCCGSD. In this setting, our network yields constant-factor reductions of approximately 50% in circuit depth and 20% in two-qubit gate count under all-to-all connectivity. For the more restricted $2\times N$ connectivity, the reductions are larger—about 55% in circuit depth and 40% in gate count. These structural improvements are accompanied by improved robustness in numerical noise simulations on the small molecular instances that are tested.

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• Quantum algorithms for chemical calculations
• Quantum circuits
• Quantum simulation