Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei

Abstract

Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of $p$-shell and $sd$-shell nuclei. Valence-space nuclear shell-model wavefunctions generated by the BIGSTICK code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the $p$-shell and 24 qubits for the $sd$-shell), from which measures of the many-body entanglement ($n$-tangles) and magic (non-stabilizerness) are determined. While exact evaluations of these measures are possible for nuclei with a modest number of active nucleons, Monte Carlo simulations are required for the more complex nuclei. The broadly-applicable Pauli-String $IZ$ exact (PSIZe-) MCMC technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wavefunctions), by factors of $\sim 8$ for some nuclei. Significant multi-nucleon entanglement is found in the $sd$-shell, dominated by proton-neutron configurations, along with significant measures of magic. This is evident not only for the deformed states, but also for nuclei on the path to instability via regions of shape coexistence and level inversion. These results indicate that quantum-computing resources will accelerate precision simulations of such nuclei and beyond.

38 pages, 15 figures

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• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• Interplay of entanglement structures and stabilizer entropy in spin models
• The non-stabilizerness of fermionic Gaussian states
• Stabilizer Scars
• Computing quantum magic of state vectors
• Operational interpretation of the Stabilizer Entropy
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Entanglement Properties of SU(2) Gauge Theory
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• The Magic Barrier before Thermalization
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Harvesting stabilizer entropy and non-locality from a quantum field
• Entanglement and magic on the light-front
• Van Hove singularities in stabilizer entropy densities
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing
• Study of entanglement in Ne, Mg, and Si isotopic chains