aiqbench analysis
This paper introduces Certified Quotient Calibration (CQC), a rigorous framework that uses statistical bounds to validate whether quantum circuit symmetries can safely reduce calibration overhead without compromising accuracy. By combining weighted-projective-space orbits with finite-shot guarantees, the method achieves significant shot savings on current hardware while explicitly accounting for noise and compilation errors. The approach represents a critical step toward scalable, resource-efficient quantum device characterization.
Certified Quotient Calibration with Weighted-Projective Orbits and Finite-Shot Guarantees
arXiv:2512.00681v2 Announce Type: replace Abstract: Periodic controls can make a quantum-calibration scan redundant, but compilation, noise, and measurement can invalidate the symmetry behind that reduction. We introduce Certified Quotient Calibration (CQC), which audits whether circuit amplitudes have a common positive grading and define weighted-projective-space (WPS) control orbits. From pilot counts it bounds the largest proposed within-orbit and smallest audited between-orbit squared Hellinger distances by U_in and L_out. CQC accepts only when these bounds meet a task tolerance, preserve audited alternatives, and imply a net saving after certification cost; otherwise it rejects or defers the reduction. The theorem bounds accepted orbit substitutions and [0,1]-valued calibration objectives on one confidence event. Its cost corollary authorizes a representative-only scan only when its certification-inclusive cost is below that of the full grid. Weighted-projective descent, Hellinger testing rates, and multinomial concentration are standard; the contribution is their combination into a finite-shot approve--reject--defer guarantee for task error and net calibration cost. Gate-level experiments on IQM Garnet and IBM Marrakesh, Kingston, and Fez exercise all three decisions in compiled one-, two-, and three-qubit families. In a preregistered two-qubit Bell-phase experiment on IBM Kingston, the pilot audit found U_in=0.01922<L_out=0.09030, and quotient and full scans selected the same correction orbit for both injected phase offsets. Fresh held-out counts met the prespecified 0.03 noninferiority margin. Including 18,432 pilot shots, the quotient procedure used 36,864 rather than 55,296 total shots, a 33.3% reduction. These results support the CQC decision path for the tested families, but not a native cubic pulse law, a device-independent WPS orbit, or a universal saving rate.
Abstract:Periodic controls can make a quantum-calibration scan redundant, but compilation, noise, and measurement can invalidate the symmetry behind that reduction. We introduce Certified Quotient Calibration (CQC), which audits whether circuit amplitudes have a common positive grading and define weighted-projective-space (WPS) control orbits. From pilot counts it bounds the largest proposed within-orbit and smallest audited between-orbit squared Hellinger distances by U_in and L_out. CQC accepts only when these bounds meet a task tolerance, preserve audited alternatives, and imply a net saving after certification cost; otherwise it rejects or defers the reduction. The theorem bounds accepted orbit substitutions and [0,1]-valued calibration objectives on one confidence event. Its cost corollary authorizes a representative-only scan only when its certification-inclusive cost is below that of the full grid. Weighted-projective descent, Hellinger testing rates, and multinomial concentration are standard; the contribution is their combination into a finite-shot approve--reject--defer guarantee for task error and net calibration cost. Gate-level experiments on IQM Garnet and IBM Marrakesh, Kingston, and Fez exercise all three decisions in compiled one-, two-, and three-qubit families. In a preregistered two-qubit Bell-phase experiment on IBM Kingston, the pilot audit found U_in=0.01922<L_out=0.09030, and quotient and full scans selected the same correction orbit for both injected phase offsets. Fresh held-out counts met the prespecified 0.03 noninferiority margin. Including 18,432 pilot shots, the quotient procedure used 36,864 rather than 55,296 total shots, a 33.3% reduction. These results support the CQC decision path for the tested families, but not a native cubic pulse law, a device-independent WPS orbit, or a universal saving rate.
19 pages, 2 figures, 8 tables. Replacement with a new title, theory, and cross-platform QPU experiments
arXiv:2512.00681 [quant-ph]
(or arXiv:2512.00681v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.00681 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 359 words
Related coverage
Quantum Natural Gradient on Quotient Spaces
arXiv · Sep 1, 2026
Certified Finite-Shot Operating Windows for Virtual Distillation and Symmetry Verification
arXiv · Jun 16, 2026
News
Quantum Computing Report · Jul 25, 2026
Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models
arXiv · Jun 5, 2026