Observable Geometry for Effective Quantum Circuits

Abstract: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.

arXiv:2607.20198 [quant-ph]

(or arXiv:2607.20198v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.20198 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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