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Condensed Matter, Strongly Correlated Electrons, cond-mat.str-el
Abstract:
Nonstabilizerness, also known as ``magic'', stands as a crucial resource for
achieving a potential advantage in quantum computing. Its connection to
many-body physical phenomena is poorly understood at present, mostly due to a
lack of practical methods to compute it at large scales. We present a novel
approach for the evaluation of nonstabilizerness within the framework of matrix
product states (MPS), based on expressing the MPS directly in the Pauli basis.
Our framework provides a powerful tool for efficiently calculating various
measures of nonstabilizerness, including stabilizer R\'enyi entropies,
stabilizer nullity, and Bell magic, and enables the learning of the stabilizer
group of an MPS. We showcase the efficacy and versatility of our method in the
ground states of Ising and XXZ spin chains, as well as in circuits dynamics
that has recently been realized in Rydberg atom arrays, where we provide
concrete benchmarks for future experiments on logical qubits up to twice the
sizes already realized.
