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
∼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.
The use of nuclear spins for quantum computation is limited by the difficulty in creating genuine quantum entanglement between distant nuclei. Current demonstrations of nuclear entanglement in semiconductors rely on coupling the nuclei to a common electron, which is not a scalable strategy. In this work, we demonstrated a two-qubit controlled-Z logic operation between the nuclei of two phosphorus atoms in a silicon device, separated by up to 20 nanometers. Each atom binds separate electrons, whose exchange interaction mediates the nuclear two-qubit gate. We prepared and measured a nuclear Bell state with a fidelity of [Formula: see text] and a concurrence of [Formula: see text]. With this method, future progress in scaling up semiconductor spin qubits can be extended to the development of nuclear spin-based quantum computers.
Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of p -shell and s d -shell nuclei. Valence-space nuclear shell-model wave functions generated by the code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the p shell and 24 qubits for the s d shell), from which measures of the many-body entanglement ( n -tangles) and magic (nonstabilizerness) 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 I ̂ Z ̂ exact (PSIZe) Markov chain Monte Carlo (MCMC) technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wave functions), by factors of ≈ 8 for some nuclei. Significant multinucleon entanglement is found in the s d 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.