Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models

TL;DR

This paper investigates the challenges and resource costs of simulating high-dimensional ground states of contextual quantum models using qubit-based quantum circuits, focusing on local approximations and permutation-symmetric encoding.

Contribution

It introduces a universal set of permutation-symmetry preserving qubit gates for simulating qutrit-based local ground states, enabling resource assessment of such simulations.

Findings

Lower energy density ground states are easier to simulate.

Permutation-symmetric encoding effectively represents qutrit local states.

Simulation accuracy depends on quantum resources and circuit iterations.

Abstract

Contextuality, one of the strongest forms of quantum correlations, delineates the quantum world and the classical one. It has been shown recently that some quantum models, in the form of infinite one-dimensional translation-invariant Hamiltonians with nearest- and next-to-nearest-neighbor interactions, have the lowest ground state energy density allowed in quantum physics. However, these models all have local Hilbert space dimension larger than two, making the study of their ground state behavior difficult on current qubit-based variational quantum simulation platforms. In this work, we focus on the cost of simulating the local approximations of ground states of these models using qubit-based parameterized quantum circuits. The local approximations, which are 3-site reduced density matrices with local Hilbert space dimension three, are purified then encoded into permutation-symmetric qubits. We develop a universal set of permutation-symmetry preserving qubit-based gates, using them as an ansatz to simulate parameterized quantum circuits designed for qutrits. These techniques allow us to assess the accuracy of simulating the purified local ground states with respect to a fixed amount of classical and quantum resources. We found that given the same quantum circuit and the number of iterations, more contextual ground states with lower energy density are easier to simulate.