Diagonal Adaptive Non-local Observables on Quantum Neural Networks

2026-05-14

AI Summary

This work addresses the challenge in conventional variational quantum algorithms where adaptive non-local observables (ANOs), while enhancing expressivity, lead to a rapid increase in the number of parameters and classical optimization costs. The authors propose diagonal ANOs—a simplified variant that relies solely on diagonal Hermitian observables. Despite this restriction, diagonal ANOs are unitarily equivalent to full ANOs and reduce the complexity of k-local observables from O(4^k) to O(2^k). This approach naturally subsumes traditional variational quantum circuits and achieves comparable function expressivity while substantially decreasing the number of tunable parameters and measurement overhead. Consequently, the method improves the scalability and practicality of quantum neural networks.

Abstract

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 $O(4^k)$ to $O(2^k)$ 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.

Problem

• Adaptive Non-local Observables
• Variational Quantum Algorithms
• quantum observables
• parameter complexity
• classical optimization cost

Innovation

• Diagonal Adaptive Non-local Observables
• Variational Quantum Algorithms
• Quantum Neural Networks
• Measurement Complexity Reduction
• Hermitian Observables