Improving fermionic variational quantum eigensolvers with Majorana swap networks

• URL: http://arxiv.org/abs/2509.07855v1
• Date: Tue, 09 Sep 2025 15:33:13 GMT
• Title: Improving fermionic variational quantum eigensolvers with Majorana swap networks
• Abstract summary: We introduce two Majorana swap network techniques for variational quantum eigensolvers.<n>First, we develop a cyclic compilation algorithm that localizes all two-particle interaction terms in a general fermionic Hamiltonian.<n>Second, we design a Majorana swap network for the UpCCGSD variational ansatz, which is already more compact than UCCGSD.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 techniques for variational quantum eigensolvers that reduce circuit depth and two-qubit gate count, thereby limiting error accumulation. First, we develop a cyclic compilation algorithm that localizes all two-particle interaction terms in a general fermionic Hamiltonian that contains $\mathcal{O}(n^4)$ such terms, using only $\mathcal{O}(n^3)$ auxiliary Majorana-swap gates, where $n$ is the number of fermionic modes. This algorithm targets all-to-all qubit connectivity (e.g., trapped-ion processors) and can be used to compactify UCCGSD circuits. Second, we design a Majorana swap network for the UpCCGSD variational ansatz, which is already more compact than UCCGSD. Our network achieves asymptotic reductions in circuit depth and gate count of approximately 50% and 20%, respectively, under all-to-all connectivity. For the more restricted $2\times N$ connectivity, the reductions are even larger -- about 55% (circuit depth) and 40% (gate count). These improvements translate directly into increased robustness to hardware noise, as demonstrated by numerical simulations on representative examples.

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