IBM researchers reported in a preprint submitted on September 11, 2026, that they had added error-detection checks to probabilistic error cancellation (PEC) and cut its inferred sampling overhead up to 63-fold. Laurin E. Fischer, Ali Javadi-Abhari, Simon Martiel, and Alireza Seif ran the experiment on ibm_aachen, a Heron r3 superconducting processor with 156 programmable qubits. The preprint has not been peer reviewed.
PEC is an error-mitigation technique. In error mitigation, researchers use extra circuit runs and classical processing to reduce the effect of noise on averaged results. Mitigation does not need the encoded qubits that error correction requires, though the two can be combined. To apply PEC, researchers learn a model of a processor’s noise, run many randomly altered copies of a circuit, and weight the results so that, on average, the errors cancel out. The sampling overhead is how many times more runs PEC needs than an unmitigated estimate to reach the same statistical precision.
The researchers made PEC cheaper without correcting any errors. By their own analysis, the combined method’s cost still grows exponentially with the rate of faults that the checks miss.
The experiment
For error detection, the team added measurements that flag many faults and threw away every run in which a check detected a fault, a step called post-selection. The researchers then applied PEC to the noise that remained. In the abstract, they wrote that the combination “reduces the inferred sampling overhead by up to a factor of 63 relative to PEC without post-selection.”
The team simulated how a transverse-field Ising model, a standard model of interacting magnetic spins, changes over time, in circuits of two, four, and six Trotter steps. Trotter steps are short time slices that a gate-based machine runs in sequence to approximate continuous change. At six steps, the circuit contained 648 two-qubit CZ gates, the processor’s native entangling operation.
The team used 49 of ibm_aachen’s physical qubits, 22 as data qubits and 27 as check qubits. It arranged the data qubits in six hexagonal cells within the heavy-hex layout, the pattern in which IBM connects the qubits on its processors. The researchers used the check qubits both to apply the Ising model’s interactions and to detect errors.
To describe the noise that remains after post-selection, the authors built what they called a spacetime Pauli-Lindblad representation from the processor’s physical noise and the check results. They validated that model on the same processor with Clifford circuits, a class that classical computers can simulate efficiently.
Results
For PEC alone, the authors inferred sampling overheads of 44.1, 1,941, and 85,545 at two, four, and six Trotter steps. For the combined method, they inferred 12.1, 122, and 1,359. They reported larger reductions in deeper circuits, those with more layers of operations: 3.7-fold at two steps, 15.9-fold at four, and 63-fold at six.
The authors computed these overheads from the learned noise model and the measured post-selection rate, the share of runs kept, instead of counting runs. They included the cost of the runs they had discarded in post-selection.
They left out the cost of a separate filter that they applied to every method alike. With it, they discarded any run that failed a final consistency check designed to catch non-Markovian errors. Non-Markovian errors depend on a processor’s earlier history.
The authors reported that 16% to 24% of runs passed the filter. At six steps, about 3.2% of all attempted runs passed both the filter and the error checks.
The team gave both methods the same number of runs at each depth, about 6.4 million at six steps. With the combined method, the team recovered the ideal, noise-free value of the mean magnetization, the average spin alignment that it tracked, within statistical uncertainty at all three depths. At six steps, the authors wrote, standalone PEC “deviates strongly from the ideal value and has a much larger uncertainty.”
Limits
The authors applied PEC only at first order, to the leading part of the remaining noise, an approach that they wrote “leaves contributions from higher-order faults.” They estimated that the resulting bias, a systematic offset in the result, was smaller than the statistical error at each depth.
The authors wrote that the sampling cost of PEC “generally grows exponentially with circuit error strength.” In the combined method, they wrote, “detected faults are removed from the PEC exponent at first order.” In the authors’ overhead formula, faults that the checks miss still count in the exponent. They wrote that combining the methods “is advantageous when this reduction outweighs the cost of syndrome rejection,” and that the 63-fold figure “includes the checked circuit’s greater width and depth.”
Related work and next steps
In a note added to the preprint, the authors cited concurrent work by Yi Yuan, Yuanchen Zhao, and Dong E. Liu, who combined error detection with PEC in a May preprint and demonstrated it in numerical simulations of Clifford circuits on encoded qubits. The IBM team distinguished its own work by its experimental validation and its hardware demonstration of non-Clifford dynamics, which fall outside the efficiently simulable Clifford class.
In a preprint first posted in July and revised in September, Martiel, Seif, Javadi-Abhari, and colleagues encoded a computation on 76 physical qubits in error-detecting spacetime codes and reported effective gate error rates 10 times lower after post-selection.
The authors listed extensions to mid-circuit measurements and to hardware running active error correction among the next steps. They wrote that mitigating the noise that remains in encoded qubits after active error correction “requires efficient higher-order expansions.”
Update, November 12, 2026: On September 15, IBM published a blog post by Javadi-Abhari, Blake Johnson, Seif, and Jennifer Janechek that cites the preprint and its “63x reduction in the inferred sampling overhead.” In the post, the authors call the detection step “post-selected quantum error correction.”
