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 wave functions 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 (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 ˆ 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 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.
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 wave functions 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 (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 ˆ 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 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.
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.
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.
Abstract Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
The shell model provides a powerful framework for nuclear structure calculations. The nucleons beyond an inert magic core are confined in a valence shell and interact through an effective two-body potential generally determined from the G-matrix method. However, the applicability of the shell model remains limited by the exponential growth of the many-body space with the number of valence nucleons and with the size of the one-body space. The quantum Monte Carlo (QMC) methods may thus be considered as a potentially attractive alternative to the direct diagonalization of the Hamiltonian matrix. The many-body problem is indeed reduced to a set of stochastic one-body problems describing independent particles in a fluctuating external field. Up to date, the QMC approaches of the shell model lead to the ground-state and the thermodynamic properties, but a detailed spectroscopy of nuclei is not reachable. Furthermore, they suffer from a common pathology of fermionic QMC methods, namely the sign/phase problem, which strongly contaminates the convergence of the calculation. In this context, we will present a new QMC method, providing the "yrast spectroscopy" of nuclei, and in which the sign/phase problem is managed through the constrained path approximation that is widely used in the ab initio nuclear calculations and in condensed matter physics.
Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the quantum magic (nonstabilizerness) in low-energy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is quantum magic and fluctuations in quantum magic, together with entanglement, that determine computational resource requirements. As a measure of fluctuations in quantum magic, and hence the severity of the exponentially scaling classical computing resource requirements, induced by scattering, the “magic power” of the 𝑆-matrix is introduced. This provides indirect experimental constraints on quantum resources required to model nuclei and dense matter using fault-tolerant quantum computers. Using experimentally determined scattering phase shifts and mixing parameters, the magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the magic in the deuteron, are found to exhibit interesting and distinct features. The Σ−-baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on in-medium decoherence.
Quantum computing is increasingly offering concrete solutions toward the simulation of nuclear structure, with the potential to overcome the exponential scaling that limits classical diagonalization methods in large spaces. A particularly efficient encoding scheme, based on collective like-nucleon pairing modes, reduces the qubit requirements by half and avoids the non-local operator strings of standard fermion-to-qubit mappings. While this quasiparticle framework provides accurate results for semimagic nuclei, it does not adequately describe open-shell systems where proton-neutron correlations become important. In this work, we apply Brillouin-Wigner perturbation theory to systematically improve the quasiparticle description of open-shell nuclei in the sd shell, reaching an energy relative error below 0.2% compared to the nuclear shell model. Furthermore, to make the effective Hamiltonian suitable for quantum simulation, we introduce a mean-field Hartree-Fock approximation of the non-quasiparticle resolvent, achieving ground-state energies typically within 2% of the exact shell-model result. This represents a systematic improvement over the bare quasiparticle Hamiltonian while remaining within the reach of near-term quantum devices.