Improved strategies for fermionic quantum simulation with global interactions

npj | quantum information Article Published in partnership with The University of New South Wales https://doi.org/10.1038/s41534-026-01223-0 Improved strategies for fermionic quantum simulation with global interactions Check for updates 1 1234567890():,; 1234567890():,; Thierry N. Kaldenbach 1 2 1 , Erik Schultheis , Niklas Stewen & Gabriel Breuil We present efficient quantum circuits for fermionic excitation operators tailored for ion trap quantum computers exhibiting the Mølmer-Sørensen (MS) gate. Such operators commonly arise in the study of static and dynamic properties in electronic structure problems using Unitary Coupled Cluster theory or Trotterized time evolution. We detail how the global MS interaction naturally suits the non-local structure of fermionic excitation operators under the Jordan-Wigner mapping and simultaneously provides optimal parallelism in their circuit decompositions. Compared to previous schemes on ion traps, our approach reduces the number of MS gates by factors of 2-, and 4, for single-, and double excitations, respectively. These improvements promise significant speedups and error reductions, which we demonstrate by characterizing our circuits under a realistic pulse-level noise model of a linear ion trap quantum processor. Among various expected use-cases of quantum computation, digital quantum simulation of fermionic many-body systems stands out as one of the most promising prospects1–3. Quantum simulations of electronic structure problems4 are expected to yield unprecedented insight in fields ranging from quantum chemistry to materials science and engineering or drug discovery5–8. This expectation stems from the capability of quantum computers to exhibit superposition and entanglement, thus efficiently storing a combinatorially large number of electronic configurations, which is the bottleneck of many classical methods1,2,4. Electronic structure problems are typically mapped to quantum computers using a fermion-to-qubit mapping. In this formalism, the state of the system is encoded as a multi-qubit state and the Hamiltonian governing the problem is encoded as a weighted sum of Pauli operators. A large focus on fermionic mappings is dedicated to the optimization of mappings towards limited connectivity devices, where typically only interactions of one or two qubits are possible. One of the most popular approaches, the Jordan-Wigner (JW) transformation9, is highly limited in its applicability on such devices due to its linear Pauli weight scaling. More sophisticated mappings can be used to tackle this obstacle, e.g., the Bravyi-Kitaev (BK) mapping10,11 which achieves logarithmic localities. However, in practice, the benefit of logarithmic Pauli weight scaling is mitigated due to the need for many SWAP gates in the transpilation for a limited hardware connectivity12. Among numerous other approaches13–17, tree-based mappings have recently proven to be particularly effective at simultaneously mitigating the Pauli weight and number of SWAP gates for specific connectivities12,18. The necessity for SWAP gates vanishes if one instead assumes a quantum device offering up-to-global interactions. Such interactions are provided on ion trap simulators19,20 featuring the Mølmer-Sørensen (MS) gate21,22, which can be used to efficiently implement non-local Pauli rotations arising under the chosen fermionic mapping. Most importantly, any Pauli rotation can be implemented using two MS gates regardless of the underlying locality23. In the context of fermionic systems, simulations leveraging the MS gate using the JW or BK mapping have been studied for dynamics in lattice models24–26 and ground state computations in quantum chemistry27–29 based on Unitary Coupled Cluster (UCC) theory30–32. The task of implementing arbitrary quantum circuits in terms of MS gates has been studied in Refs. 33,34. While ref. 34 already provides tight bounds on the number of MS gates for generic circuits, their algorithm gets outperformed by handcrafted results for specific unitaries33,35,36. The schemes presented in our work are specific to classes of unitaries in fermionic systems. In this work, we show how the MS gate naturally implements the Pauli operator pool of fermionic and qubit excitation operators with maximum parallelism. Our approach exploits that specific types of MS gates perform simultaneous diagonalization of certain Pauli operators arising for excitation operators under the JW transformation. Using this feature, we leverage previous works, where each non-local Pauli operator is realized by its own pair of MS gates23–25,28, and achieve an MS gate reduction by a factor of 2 for quadratic terms, and a factor of 4 for quartic terms. Our technique is also ancilla-free, making it not only faster, but also cheaper in terms of qubit requirements. By exploiting the local fermionic equivalences between (anti-) 1 Institute of Materials Research, German Aerospace Center (DLR), Cologne, Germany. 2Institute for Applied Physics, Technical University of Darmstadt, e-mail: Darmstadt, Germany. npj Quantum Information | (2026)12:54 1 Article https://doi.org/10.1038/s41534-026-01223-0 Fig. 1 | Circuit for digital quantum simulation with MS gates. Circuit decomposition of the global rotation UðφÞ ¼ expðiφ=2ZÞ using the XX gate. The rotation angle in the circuit is defined as e ¼ ð1Þm φ, where m follows the distinction φ between even qubit numbers n = 2m and odd numbers n = 2m + 1 from equation (6). Gates with dashed lines are only required if n is even to turn Yj into Zj. symmetrized excitation operators, we can use our circuits as building blocks for both UCC calculations, as well as the time evolution of electronic structure Hamiltonians in second quantization37. This enables the study of mixed quantum-classical dynamics within the Born-Oppenheimer approximation, thus providing an hybrid framework for studying timedependent properties in molecules6,37–39. After introducing the fermionic building blocks, we explicitly outline our techniques at hand of the H 3 þ molecule by showing how UCCSD-, and time evolution circuits can be efficiently assembled. Finally, we demonstrate the efficiency of our circuit decompositions by characterizing the circuits via noisy simulations of molecular ground states of various molecules on an 12-qubit ion trap emulator at the pulse level. Before presenting the results, we provide short introductions into general digital quantum simulations with MS gates, and the classes of fermionic operators used in UCCSD and Hamiltonian simulation. Readers with strong familiarity with those subjects are encouraged to skip to the results. We first introduce the core properties of the MS gate and how to employ it to implement arbitrary Pauli rotations. For now, it is instructive to treat the MS gate as an idealized theoretical building block for quantum circuits, while an experimental description of the MS gate and its experimental challenges is later intro (...truncated)