Near-term fermionic simulation with subspace noise tailored quantum error mitigation

npj | quantum information Article Published in partnership with The University of New South Wales https://doi.org/10.1038/s41534-026-01248-5 Near-term fermionic simulation with subspace noise tailored quantum error mitigation Check for updates 1,2 1,3 1 1,2 1 1234567890():,; 1234567890():,; Miha Papič , Manuel G. Algaba , Emiliano Godinez-Ramirez , Inés de Vega , Adrian Auer , Fedor Šimkovic IV1 & Alessio Calzona1 Quantum error mitigation (QEM) has emerged as a powerful tool for the extraction of useful quantum information from quantum devices. Here, we introduce the Subspace Noise Tailoring (SNT) algorithm, which efficiently combines the cheap cost of Symmetry Verification (SV) and low bias of Probabilistic Error Cancellation (PEC) QEM techniques. We study the performance of our method by simulating the Trotterized time evolution of the spin-1/2 Fermi-Hubbard model (FHM) using a variety of local fermionto-qubit encodings, which define a computational subspace through a set of stabilizers, the measurement of which can be used to post-select noisy quantum data. We study different combinations of QEM and encodings and uncover a rich state diagram of optimal combinations, depending on the hardware performance, system size and available shot budget. We then demonstrate how SNT extends the reach of current noisy quantum computers in terms of the number of fermionic lattice sites and the number of Trotter steps, and quantify the required hardware performance beyond which a noisy device may compete with current state-of-the-art classical computational methods. The simulation of fermionic quantum systems from condensed matter physics and quantum chemistry is believed to provide some of the most promising applications where quantum computers are expected to eventually outperform their classical counterparts1,2. This belief is largely centered around the task of time-evolving quantum systems, which is one of the few cases where exponential quantum speedup has been proven3. This optimism has sparked a series of proof-of-principle experimental realizations on current quantum devices4–18, leading to the question of the ultimate reach of near-term, non-error-corrected quantum computations19. This question is of essential relevance given that, despite steady recent progress and ambitious company road-maps, current quantum-error-correction (QEC) experiments are still limited to small-distance codes and few logical qubits, and fully fault-tolerant quantum computers will not come into existence for a number of years to come. Recently, effort has been invested into resource estimation for the simulation of fermionic Hamiltonians on quantum hardware in terms of the required circuit depth and gate counts20–23. It has become increasingly clear that any successful application on current noisy hardware will necessitate the use of quantum error mitigation (QEM) techniques, which reduce the effects of hardware noise at the cost of an exponential increase in the number of circuit executions. A myriad of different QEM approaches have been developed24, where different techniques can be characterized by their measurement overhead, referred to as the cost of error mitigation, and their accuracy in the limit of infinite resources, referred to as the bias. Broadly speaking, approaches with low bias incur higher costs, and vice versa. The community is thus actively exploring error mitigation techniques that strike the right balance between these two factors, with the conjecture that optimal QEM strategies will likely involve hybrid approaches that combine multiple methods, leveraging their complementary strengths24. One family of commonly utilized QEM techniques is based on symmetry verification (SV)25–29. Given that quantum systems conserve certain quantities, such as the total number of fermions, it is sometimes possible to filter out measurements of a noisy quantum state that fall outside of the correct symmetry-preserving subspace8,11. Generally, these methods exhibit low cost and high bias, as only a few global symmetries exist in most systems of interest. It is possible to artificially add further symmetries for SV purposes by enlarging the computational space of the system, thus allowing the implementation of SV methods using post-selection (PS) based on the measurement of stabilizer operators, identical to syndrome measurements in QEC codes25,30. Notably, the existence of many local stabilizers is a natural 1 IQM Quantum Computers, Munich, Germany. 2Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Munich, Germany. 3PhD Programme in Condensed Matter Physics, Nanoscience and Biophysics, Doctoral School, Universidad Autónoma de Madrid, e-mail: Madrid, Spain. npj Quantum Information | (2026)12:72 1 Article https://doi.org/10.1038/s41534-026-01248-5 Fig. 1 | Classical and quantum limits of the simulability of the 2D FHM. Left: The maximal number of Trotter steps achievable for a given QEM method at a fixed TQG fidelity, and a fixed 5% rootmean-squared error (RMSE) of the site occupations. For more details see “Methods''. Right: The required TQG fidelity for the simulation of a given FHM with SNT. The dotted region represents the approximate reach of classical computations whereas the gradual onset of transparency represents a transitional regime where quantum or classical methods are in close competition, as argued in detail in Supplementary Note 190–92. feature of local fermion-to-qubit encodings22,31–35, where ancilla qubits are introduced to resolve fermionic commutation relations in a way that avoids high-weight logical operators, which would otherwise appear in standard fermion-to-qubit encodings such as the Jordan-Wigner transformation (JW)36,37. This led to stabilizer-based QEM33–35 and partial QEC35,38–40 proposals, especially on fermionic systems defined on periodic lattices in two and three dimensions14. Nonetheless, any symmetry-based QEM technique ultimately suffers from a bias due to undetectable errors, which occur within the correct subspace and thus commute with all available stabilizers. In contrast, the probabilistic error cancellation (PEC) method is, at least in principle, able to cancel any type of errors by averaging over many different circuits designed to compensate for previously characterized hardware noise41,42. However, the overhead associated with a successful PEC implementation is often prohibitively large, up to orders of magnitude larger compared to biased QEM methods19,43. A naturally arising question is therefore whether PS and PEC can be combined in a way to overcome these challenges and improve the overall performance. The initial approach of ref. 29 proposed a scheme where the errors of a two-qubit gate (TQG) were classified as (un)detectable based on total fermion parity conservation. However, a more general fermionic simulation algorithm may contain more than one stabilizer symmetry an (...truncated)