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Kun Wang Uses Adaptive Checks to Bound Stabilizer Fidelity
Kun Wang’s paper describes an adaptive method for narrowing the range of fidelities consistent with stabilizer measurements. Simulations reported in the paper compare the method with uniform random gauge selection, while also examining how
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In simulations of 51 eight-qubit cases with structured errors, an adaptive protocol reached a target fidelity-interval width in a median of seven rounds, compared with ten for uniform random measurement gauges. Kun Wang’s paper was accepted on October 7, 2026, and published in Physical Review A on October 26, 2026. It describes a method for narrowing the range of fidelities consistent with stabilizer measurements. The result is a certification technique, not a report of a new quantum processor or an improvement to a prepared state.
From one fixed gauge to an adaptive choice
Stabilizer-state experiments assess a prepared state by measuring Pauli operators that define a target state. A gauge is a choice of independent stabilizer generators used for those measurements. Earlier work established an optimal worst-case lower fidelity bound for data from one fixed gauge, but that data can still leave a wide range of possible fidelities.
Wang’s method adds a complementary upper bound, producing a certified interval rather than only a lower limit. After each round, the protocol uses the accumulated measurement results to find two compatible syndrome distributions that mark the interval’s endpoints. It then selects a new gauge based on which stabilizer measurements most sharply distinguish those endpoint cases.
“We develop an adaptive extension that reports the full certified fidelity interval.”
Kun Wang, paper author
Seven rounds in a small-scale benchmark
The comparison used exact expectation values, an eight-qubit GHZ target, and a stopping threshold of 0.01 for the interval width. In the structured benchmark, each of 51 cases had an affine-support syndrome distribution with dimension four. Adaptive witness elimination reached the threshold in a median of seven rounds; one case had not reached it by the ten-round cutoff. Under uniform random gauge selection, the median was ten rounds and 25 of 51 cases missed the threshold by that cutoff.
A second benchmark used 51 full-support syndrome distributions. Adaptive selection reached the same threshold in a median of 25 rounds, with no misses among the 51 trials by the tested cutoff of 32 rounds. Uniform random selection did not reach the threshold in the median run, and all 51 trials missed it by that cutoff. Those figures describe simulated instances, not performance measured on a quantum device.
Finite samples and the exponential cost
Real measurements use finite numbers of shots, so estimates carry statistical uncertainty. Wang’s simulations include shot noise and report that the certified intervals retain the true fidelity in at least 50 of 51 trials across the plotted shot budgets. As the number of shots rises, the interval’s statistical floor falls; additional adaptive rounds cannot remove uncertainty caused by finite data.
The paper also sets a hard limit on what adaptivity can guarantee. For arbitrary states, exact fidelity determination may require querying all 2n − 1 nontrivial stabilizers, or at least ceiling((2n − 1)/n) full gauge rounds in the worst case. Structured syndrome distributions can need far fewer measurements, but that speedup depends on the structure being present.
The computation poses a separate scaling problem: the exact optimization represents 2n syndrome probabilities and solves linear programs over them. The paper’s numerical tests therefore demonstrate the selection strategy on small systems, rather than large-scale classical tractability. For now, the certified bounds are exact for the data considered, while extending the optimization beyond its exponential cost remains an untested step.