AI 中文总结
该研究从李群代数和几何观点出发，研究变分量子电路冗余性与有效性，通过稳定子群分解等方法刻画有效电路自由度，得出易于处理的计算标准并经数值实验验证。
AI 中文摘要
我们通过李群的代数和几何观点研究变分量子电路的冗余性和有效性。考虑作用于厄米可观测量的酉变换，给出了稳定子群分解。随后，我们将厄米轨道与对称空间的商空间等同起来。通过这种联系，我们刻画了有效电路的自由度。我们的谱分解和齐性空间方法产生了易于处理的计算标准，并通过数值实验得到验证。
英文摘要
We study redundancy and effectiveness of Variational Quantum Circuits via algebraic and geometric views of Lie groups. Considering unitary transformations acting on Hermitian observables, a stabilizer group decomposition is given. Subsequently, we identify the Hermitian orbit with a quotient space of a symmetric space. Through this connection, we characterize the effective circuit degrees of freedom. Our approach of spectral decompositions and homogeneous spaces yields tractable calculation criteria, which are verified by numerical experiments.
CommentsAccepted at QCE26 Workshop
