Variational ground state for Shell Model Hamiltonians

In this work, we compare three qubit-mapping strategies to study the structure of the nuclear ground state within the shell model description employing the Variational Quantum Eigensolver (VQE) approach. Although the initial point for different mappings is a Hamiltonian matrix in many-body particle basis or Slater determinant (SD) basis, the structure of the trial wavefunction and resource counts are different for each mapping. These three mappings are tested for a mid $p$ -shell nucleus $^{10}$ B and compared the quantum resources required to find the ground state for each mapping. Further, we extend the qubit-efficient mapping to study the ground state of one more mid $p$ -shell nucleus $^{12}$ C. We run circuits up to 26-qubits representing their ground states on a noisy simulator (IBM's FakeFez backend) and quantum hardware ( $ibm\_fez$ ). The best post-error mitigated results from the hardware for $^{10}$ B ground state is obtained following SD to qubit mapping with a percent error of 0.21 \%. The percent errors for the same state following cSD and pnSD mapping are 3.37 and 8.88 \%, respectively. On the other hand, following the cSD mapping, the post-error mitigated ground state energy of $^{12}$ C is 6.82 \% away from the exact result. We further evaluate the fidelity of the VQE wavefunctions obtained from hardware with respect to the shell model wavefunctions for the cSD mapping. This cSD mapping can be useful for scaling the VQE algorithm for complex nuclei across different mass regions in terms of qubit efficiency.In this work, we compare three qubit-mapping strategies to study the structure of the nuclear ground state within the shell model description employing the Variational Quantum Eigensolver (VQE) approach. Although the initial point for different mappings is a Hamiltonian matrix in many-body particle basis or Slater determinant (SD) basis, the structure of the trial wavefunction and resource counts are different for each mapping. These three mappings are tested for a mid $p$-shell nucleus $^{10}$B and compared the quantum resources required to find the ground state for each mapping. Further, we extend the qubit-efficient mapping to study the ground state of one more mid $p$-shell nucleus $^{12}$C. We run circuits up to 26-qubits representing their ground states on a noisy simulator (IBM's FakeFez backend) and quantum hardware ($ibm\_fez$). The best post-error mitigated results from the hardware for $^{10}$B ground state is obtained following SD to qubit mapping with a percent error of 0.21 \%. The percent errors for the same state following cSD and pnSD mapping are 3.37 and 8.88 \%, respectively. On the other hand, following the cSD mapping, the post-error mitigated ground state energy of $^{12}$C is 6.82 \% away from the exact result. We further evaluate the fidelity of the VQE wavefunctions obtained from hardware with respect to the shell model wavefunctions for the cSD mapping. This cSD mapping can be useful for scaling the VQE algorithm for complex nuclei across different mass regions in terms of qubit efficiency.

nucl-thCross-listedarXiv:2605.30261May 29, 20260 citations

Shell-model study of58Ni using quantum computing algorithm

Bharti Bhoy, P. D. Stevenson

Abstract This study presents a simulated quantum computing approach for the investigation into the shell-model energy levels of58Ni through the application of the variational quantum eigensolver (VQE) method in combination with a problem-specific ansatz. The primary objective is to achieve a fully accurate low-lying energy spectrum of58Ni. The chosen isotope,58Ni is particularly interesting in nuclear physics through its role in astrophysical reactions while also being a simple but non-trivial nucleus for shell-model study, it being two particles outside a closed shell. Our ansatz, along with the VQE method are shown to be able to reproduce exact energy values for the ground state and first and second excited states. We compare a classical shell model code, the values obtained by diagonalization of the Hamiltonian after qubit mapping, and a noiseless simulated ansatz+VQE simulation. The exact agreement between classical and qubit-mapped diagonalization shows the correctness of our method, and the high accuracy of the simulation means that the ansatz is suitable to allow a full reconstruction of the full nuclear wave function.Abstract This study presents a simulated quantum computing approach for the investigation into the shell-model energy levels of58Ni through the application of the variational quantum eigensolver (VQE) method in combination with a problem-specific ansatz. The primary objective is to achieve a fully accurate low-lying energy spectrum of58Ni. The chosen isotope,58Ni is particularly interesting in nuclear physics through its role in astrophysical reactions while also being a simple but non-trivial nucleus for shell-model study, it being two particles outside a closed shell. Our ansatz, along with the VQE method are shown to be able to reproduce exact energy values for the ground state and first and second excited states. We compare a classical shell model code, the values obtained by diagonalization of the Hamiltonian after qubit mapping, and a noiseless simulated ansatz+VQE simulation. The exact agreement between classical and qubit-mapped diagonalization shows the correctness of our method, and the high accuracy of the simulation means that the ansatz is suitable to allow a full reconstruction of the full nuclear wave function.

arXiv:2402.15577New Journal of PhysicsJun 12, 202417 citations

Variational Ground States of the Holstein Hamiltonian

Yang Zhao

Jan 1, 19940 citations

Treatment of the like-particle pairing of quartets

M Sambataro, Nicolae Sandulescu

The ground state correlations induced by a general pairing Hamiltonian in a finite system of like fermions are described in terms of four-body correlated structures (quartets). These are real superpositions of the products of two pairs of particles in time-reversed states. Quartets are determined variationally through an iterative sequence of diagonalizations of the Hamiltonian in restricted model spaces and are, in principle, all distinct from one another. The ground state is represented as a product of quartets to which, depending on the number of particles (supposed to be even, in any case), an extra collective pair is added. The extra pair is also determined variationally. In the case of pairing in a spherically symmetric mean field, both the quartets and the extra pair (if any) are characterized by a total angular momentum J = 0. Realistic applications of the quartet formalism are carried out for Sn isotopes with valence neutrons in the 50–82 neutron shell. The exact ground state correlation energies, occupation numbers and pair transfer matrix elements are reproduced to a very high degree of precision. The formalism also lends itself to a straightforward and accurate description of the lowest seniority 0 and 2 excited states of the pairing Hamiltonian. A simplified representation of the ground state as a product of identical quartets is eventually discussed and found to improve considerably upon the more traditional particle-number projected BCS approach.The ground state correlations induced by a general pairing Hamiltonian in a finite system of like fermions are described in terms of four-body correlated structures (quartets). These are real superpositions of the products of two pairs of particles in time-reversed states. Quartets are determined variationally through an iterative sequence of diagonalizations of the Hamiltonian in restricted model spaces and are, in principle, all distinct from one another. The ground state is represented as a product of quartets to which, depending on the number of particles (supposed to be even, in any case), an extra collective pair is added. The extra pair is also determined variationally. In the case of pairing in a spherically symmetric mean field, both the quartets and the extra pair (if any) are characterized by a total angular momentum J = 0. Realistic applications of the quartet formalism are carried out for Sn isotopes with valence neutrons in the 50–82 neutron shell. The exact ground state correlation energies, occupation numbers and pair transfer matrix elements are reproduced to a very high degree of precision. The formalism also lends itself to a straightforward and accurate description of the lowest seniority 0 and 2 excited states of the pairing Hamiltonian. A simplified representation of the ground state as a product of identical quartets is eventually discussed and found to improve considerably upon the more traditional particle-number projected BCS approach.

arXiv:1303.4553Journal of Physics G Nuclear and Particle PhysicsApr 9, 201317 citations

Comments on variational ground states for lattice hamiltonians

Ramesh Anishetty, Anton Bovier

Physics Letters BFeb 1, 19841 citation

p

-shell nucleus

^{10}

B and compared the quantum resources required to find the ground state for each mapping. Further, we extend the qubit-efficient mapping to study the ground state of one more mid

p

-shell nucleus

^{12}

C. We run circuits up to 26-qubits representing their ground states on a noisy simulator (IBM's FakeFez backend) and quantum hardware (

ibm\_fez

). The best post-error mitigated results from the hardware for

^{10}

B ground state is obtained following SD to qubit mapping with a percent error of 0.21 \%. The percent errors for the same state following cSD and pnSD mapping are 3.37 and 8.88 \%, respectively. On the other hand, following the cSD mapping, the post-error mitigated ground state energy of

^{12}

C is 6.82 \% away from the exact result. We further evaluate the fidelity of the VQE wavefunctions obtained from hardware with respect to the shell model wavefunctions for the cSD mapping. This cSD mapping can be useful for scaling the VQE algorithm for complex nuclei across different mass regions in terms of qubit efficiency.