Merged amplitude encoding for Chebyshev quantum Kolmogorov--Arnold networks: trading qubits for circuit executions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918448072753152 |
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| author | Wakaura, Hikaru |
| author_facet | Wakaura, Hikaru |
| contents | Quantum Kolmogorov--Arnold networks based on Chebyshev polynomials (CCQKAN) evaluate each edge activation function as a quantum inner product, creating a trade-off between qubit count and the number of circuit executions per forward pass. We introduce merged amplitude encoding, a technique that packs the element-wise products of all $n$ input-edge vectors for a given output node into a single amplitude state, reducing circuit executions by a factor of $n$ at a cost of only 1--2 additional qubits relative to the sequential baseline. The merged and original circuits compute the same mathematical quantity exactly; the open question is whether they remain equally trainable within a gradient-based optimization loop. We address this question through numerical experiments on 10 network configurations under ideal, finite-shot, and noisy simulation conditions, comparing original, parameter-transferred, and independently initialized merged circuits over 16 random seeds. Wilcoxon signed-rank tests show no significant difference between the independently initialized merged circuit and the original ($p > 0.05$ in 28 of 30 comparisons), while parameter transfer yields significantly lower loss under ideal conditions ($p < 0.001$ in 9 of 10 configurations). On 10-class digit classification with the $8\times8$ MNIST dataset using a one-vs-all strategy, original and merged circuits achieve comparable test accuracies of 53--78\% with no significant difference in any configuration. These results provide empirical evidence that merged amplitude encoding preserves trainability under the simulation conditions tested. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Merged amplitude encoding for Chebyshev quantum Kolmogorov--Arnold networks: trading qubits for circuit executions Wakaura, Hikaru Quantum Physics Quantum Kolmogorov--Arnold networks based on Chebyshev polynomials (CCQKAN) evaluate each edge activation function as a quantum inner product, creating a trade-off between qubit count and the number of circuit executions per forward pass. We introduce merged amplitude encoding, a technique that packs the element-wise products of all $n$ input-edge vectors for a given output node into a single amplitude state, reducing circuit executions by a factor of $n$ at a cost of only 1--2 additional qubits relative to the sequential baseline. The merged and original circuits compute the same mathematical quantity exactly; the open question is whether they remain equally trainable within a gradient-based optimization loop. We address this question through numerical experiments on 10 network configurations under ideal, finite-shot, and noisy simulation conditions, comparing original, parameter-transferred, and independently initialized merged circuits over 16 random seeds. Wilcoxon signed-rank tests show no significant difference between the independently initialized merged circuit and the original ($p > 0.05$ in 28 of 30 comparisons), while parameter transfer yields significantly lower loss under ideal conditions ($p < 0.001$ in 9 of 10 configurations). On 10-class digit classification with the $8\times8$ MNIST dataset using a one-vs-all strategy, original and merged circuits achieve comparable test accuracies of 53--78\% with no significant difference in any configuration. These results provide empirical evidence that merged amplitude encoding preserves trainability under the simulation conditions tested. |
| title | Merged amplitude encoding for Chebyshev quantum Kolmogorov--Arnold networks: trading qubits for circuit executions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.02818 |