The Signal
IBM VQE Tests Find Error Bars Missed Energy Residuals by Up to 32×
A study of molecular energy evaluations on IBM’s Aachen and Pittsburgh quantum processors found raw VQE residuals for oxygen and beryllium hydride reached 12 to 32 times the reported statistical uncertainty. The 110-job study also found tha
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A 32-fold gap on Pittsburgh
A paper posted to arXiv on October 28 reports that statistical uncertainty estimates understated measured molecular-energy residuals by as much as a factor of 32 in tests on IBM quantum processors. Julen Larrucea compared calculations on IBM’s 156-qubit Heron processors Aachen and Pittsburgh, finding the largest gap for beryllium hydride on Pittsburgh: the average residual was 685 millihartree, against a mean reported uncertainty of 21.64 millihartree.
“A smaller statistical error bar need not mean a more accurate molecular energy,” Larrucea writes in the paper. The study examines a narrow but important part of a variational quantum eigensolver (VQE): measuring energy after parameters have been optimized, rather than running the optimization itself on quantum hardware. Julen Larrucea, “Execution bias, repeatability and mitigation cost in parameter-frozen molecular VQE energy evaluation”
Frozen circuits isolate hardware execution
Larrucea first optimized molecular states noiselessly, then froze their parameters, layouts and compiled circuits for hardware runs. The experiment covered five molecules in a pilot and a repeated three-molecule cohort—lithium hydride, oxygen and beryllium hydride—along with known-state controls. In total, it comprised 110 jobs and 28.2 minutes of billed quantum processing time; the isolated cohort ran across three time windows within a 31.7-hour campaign.
The reported 12-to-32-fold gaps apply to raw 1,024-shot measurements of oxygen and beryllium hydride. For oxygen, mean residuals were 119 millihartree on Aachen and 250 millihartree on Pittsburgh, compared with mean returned uncertainties of about 10 and 13 millihartree. The beryllium hydride results were larger: 452 millihartree on Aachen and 685 millihartree on Pittsburgh. These residuals measure execution error against the ideal energy of each frozen state, not the complete error against the energy of a real molecule.
More shots did not remove the bias
Repeated jobs showed why a single run’s statistical bar can give an incomplete account. For Pittsburgh beryllium hydride, the six-job sample standard deviation reached 120.4 millihartree—5.6 times the mean reported uncertainty. Raising the nominal shot count from 1,024 to 4,096 reduced the returned uncertainty, but did not reliably remove the offset or the variation between jobs.
Mitigation also produced mixed results. Zero-noise extrapolation reduced oxygen’s absolute residual by 49.7% on Aachen and 83.5% on Pittsburgh, at about four times the charge of a raw 1,024-shot job. On Pittsburgh, twirled readout error extinction reduced oxygen’s residual by 80 millihartree per raw-job charge, compared with 50 millihartree for zero-noise extrapolation; on Aachen, the per-charge comparison reversed. For beryllium hydride, twirled readout error extinction slightly increased the mean residual on both processors.
Two processors, three windows—and clear limits
The paper also flags a hardware-control issue: known-state tests on Aachen’s qubit 124 found preparation or readout responses 5.4 to 5.6 times the calibration estimate. Thirteen mitigated energy estimates fell outside the mapped operator spectrum, while none of the raw estimates did. Such results are diagnostics of these runs, not evidence that all mitigated estimates—or IBM processors generally—behave this way.
The author describes the statistical analyses as exploratory. The evidence comes from two processors and three temporal windows; the mitigation arms ran in a fixed order, which can confound treatment effects with changes over time. No optimization loop ran on the hardware, leaving optimizer–hardware feedback outside the test. Larrucea’s recommendation is specific to the measured problem: check workload behavior and repeat measurements before spending additional QPU time on more shots.