Cost of locally approximating high-dimensional ground states of contextual quantum models

Contextuality, one of the strongest forms of quantum correlations, delineates the boundary between the quantum world and the classical one. Recent advances show that some translation-invariant contextuality witnesses are maximally violated by ground states and local observables of infinite one-dimensional translation-invariant Hamiltonians. However, these models all have local Hilbert space dimension larger than two, making the study of their ground states behavior difficult on current qubit-based platforms. In this work, we focus on the cost of simulating their 3-site reduced density matrices using qubit-based parameterized quantum circuits. The local approximations are purified then encoded into permutation-symmetric qubit states. By developing a universal set of permutation-symmetry preserving qubit-based gates, we assess the accuracy of simulating the purified local ground states against fixed classical and quantum resources. Results reveal that more contextual ground states with lower energy density are easier to simulate under identical resources. The authors encode qutrit contextual-Hamiltonian ground states into permutation-symmetric qubits with symmetry-preserving gates and use parameterized quantum circuits to variationally simulate their purified 3-site reduced states. They find that stronger contextuality reduces simulation cost, although all contextual states cost more than non-contextual ones.