# Statevector-to-Hardware Reconstruction of a Four-Qubit ZZ Quantum Kernel: A Single-Backend Case Study of Three Execution Jobs

arXiv: https://arxiv.org/abs/2607.20377 · HTML: https://mlsanity.com/paper/2607.20377/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 22 Jul 2026.

## Builds on (most cited first, 18 of 18)

- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Grounding Representation Similarity with Statistical Testing](https://mlsanity.com/paper/2108.01661/) (2021)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [On the expressivity of embedding quantum kernels](https://mlsanity.com/paper/2309.14419/) (2023)
- [Automatic and effective discovery of quantum kernels](https://mlsanity.com/paper/2209.11144/) (2022)
- [Benchmarking MedMNIST dataset on real quantum hardware](https://mlsanity.com/paper/2502.13056/) (2025)
- [Shot-frugal and Robust quantum kernel classifiers](https://mlsanity.com/paper/2210.06971/) (2022)
- [AQKA: Active Quantum Kernel Acquisition Under a Shot Budget](https://mlsanity.com/paper/2605.14672/) (2026)
- [Benchmarking Quantum Kernel Support Vector Machines Against Classical Baselines on Tabular Data: A Rigorous Empirical Study with Hardware Validation](https://mlsanity.com/paper/2604.18837/) (2026)

## Abstract (arXiv)

Hardware noise and finite sampling perturb the fidelity estimates forming a quantum-kernel Gram matrix. We measured how far three hardware-reconstructed Gram matrices depart from an exact statevector reference for one frozen four-qubit ZZ feature map on N=24 indoor air-quality windows, executed on ibm_fez at 1024 shots per circuit in three single, non-interleaved jobs: baseline, dynamical decoupling alone, and gate twirling alone. All were complete, finite, and positive-semidefinite. Off-diagonal root-mean-squared error (RMSE) against the reference was 0.0878, 0.0864, and 0.0427; full-matrix centered kernel alignment (CKA) ranged 0.933-0.989 and the post hoc diagonal-excluded (U-centered) CKA 0.816-0.986. The gate-twirled job deviated least on every reported geometry axis; its baseline contrasts are deletion-stable for the Spearman, mean-absolute-error, RMSE, and full-matrix CKA diagnostics, while the Pearson and diagonal-excluded contrasts fall just below that convention. Dynamical decoupling was not separated from the baseline. The observed error exceeded both finite-shot reference scales, so, under those sampling-only models, sampling does not explain it. Centered kernel-target alignment did not track reconstruction fidelity and stayed at or below each label-permutation reference: implementation fidelity and task relevance are distinct diagnostic axes. All configuration-level statements describe three realized jobs on one backend; no mitigation-efficacy, classifier-superiority, forecasting, or quantum-advantage claim is made.