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Diagonal Adaptive Non-local Observables on Quantum Neural Networks

arXiv 2605.15410 ↗First posted 14 May 2026quant-ph cs.AI cs.LGcited by 0

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Abstract (arXiv)

Adaptive Non-local Observables (ANOs) have shown that making quantum observables dynamic can substantially enlarge the function space of Variational Quantum Algorithms, partly shifting hardware demands from circuit synthesis to measurement design. However, this advantage is accompanied by a steep increase in the number of parameters, as well as the classical optimization cost for varying general Hermitian observables. We propose a special form of ANO that significantly reduces this burden by considering only diagonal observables paired with quantum circuits. Mathematically, this is equivalent to the full ANO of a large parameter space since diagonal matrices are canonical representatives of the ANO space modulo unitary similarity. As a result, Diagonal ANO retains the same capability of full ANO while reducing k-local observable complexity from O(4k) to O(2k) and lowering the corresponding measurement-side classical computation. In this sense, diagonal ANO preserves much of the benefit of full ANO while encompassing conventional VQCs as a special case.

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References · 12

  1. 2020Variational Quantum Algorithmscited by 692
  2. 2018Barren plateaus in quantum neural network training landscapescited by 630
  3. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  4. 2016Quantum Machine Learningcited by 326
  5. 2020Quantum Convolutional Neural Networks for High Energy Physics Data Analysiscited by 64
  6. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 51
  7. 2023Asynchronous training of quantum reinforcement learningcited by 20
  8. 2025Learning to Measure Quantum Neural Networkscited by 15
  9. 2025Adaptive Non-local Observable on Quantum Neural Networkscited by 7
  10. 2025Quantum Reinforcement Learning by Adaptive Non-local Observablescited by 5
  11. 2026Quantum Super-resolution by Adaptive Non-local Observablescited by 4
  12. 2023Breaking the cubic barrier in the Solovay-Kitaev algorithmcited by 2

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