Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.12798 · Acta Physica Polonica B Proceedings Supplement

Single-step Quantum Simulation of Two Nucleons

Bhoomika Maheshwari, Paul Stevenson, P. Van Isacker

nucl-thhep-thnucl-exquant-phSubmitted Dec 14, 2025• Announced Dec 16, 2025• 1 citation
arXivHTMLPDF

Abstract

Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver (SSVQE) combined with an adaptive derivative-assembles pseudo-trotter (ADAPT) ansatz to obtain the low-lying states of any nuclear system in a single optimization run. As an example, we apply this method in this work to a trivial identical nucleon system, two nucleons in the $0p_{3/2}$ orbital, mapped to 4 qubits depicting m-scheme single-particle states including a surface delta effective interaction using the Jordan-Wigner transformation. The ADAPT-SSVQE algorithm, by utilizing a symmetry-preserving double-excitation ADAPT operator pool, uniquely optimizes a weighted energy sum, forcing the simultaneous convergence of two lowest states within the total angular momentum $M_J=0$ subspace. We demonstrate the accuracy of the method by benchmarking against the exact diagonalization, confirming its potential for probing nuclear structure and pairing phenomena on current and near-future quantum devices without requiring multi-step procedure for excited states.

Comments
To Appear in Acta Physica Polonica B (Special Issue dedicated to Mazurian Lakes Conference 2025)

Related papers

Full-Spectrum Quantum Simulation for the Nuclear Shell Model

B. Maheshwari, P. Stevenson, P. Van Isacker

The nuclear shell model is a general way of expressing the many-body nuclear Hamiltonian and deciphering the underlying nuclear structure. In today's era of modern and high-power computation, the primary limitation of the nuclear shell model is the enormous dimensionality of its Hilbert space, which far exceeds available storage capacity and prevents the diagonalization of the full Hamiltonian matrix in that space. Quantum computing offers a scalable solution to bypass this curse of dimensionality. In this work, we introduce a single-run quantum simulation capable of obtaining multiple shell-model eigenstates simultaneously. The nuclear Hamiltonian is transformed from a bit to a qubit basis using the Jordan-Wigner transformation, explicitly preserving fermionic anti-commutation. We employ a Subspace Search Variational Quantum Eigensolver (SSVQE) along with an Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansatz to construct the quantum circuit required to solve the shell-model problem. The ADAPT-SSVQE algorithm uses a symmetry-preserving single and double-excitation operator pool and optimizes a weighted energy sum to obtain the simultaneous convergence of all eigenstates within a targeted MJ subspace, eliminating the need for post-processing efforts to extract excited spectra. We benchmark this approach by solving the problem for two and three identical nucleons in a j = 9/2 orbital, successfully extracting five and ten mutually orthogonal states, respectively, within a 10-qubit active space. The algorithm achieves spectroscopic accuracy, in simulation, relative to exact diagonalization and intrinsically restores total angular momentum (\hat{J}^2) symmetry.

nucl-thCross-listedarXiv:2607.08235•Jul 10, 2026•0 citations

Excited states from ADAPT-VQE convergence path in many-body problems: Application to nuclear pairing problem and H 4 molecule dissociation

Jing Zhang, Denis Lacroix A

A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems. The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) towards the ground state of the many-body problem. This method is shown to be accurate with only a small overhead in terms of quantum resources required to get the ground state. We also show that the quantum algorithm might be used to facilitate the convergence of the ADAPT-VQE method itself. Successful applications of the technique are made to like-particle pairing as well as neutron-proton pairing. Finally, the H 4 molecule’s dissociation also illustrates the technique, demonstrating its accuracy and versatility.

arXiv:2506.22275•Physics Letters B•Aug 23, 2025•3 citations

Comparison of variational quantum eigensolvers in light nuclei

Miquel Carrasco-Codina, Emanuele Costa, Antonio Márquez Romero +2 more

Quantum computing is one of the most promising technologies of the near future, and the simulation of quantum many-body systems is a natural application. In this work, we present classical simulations of the ground states of light atomic nuclei within the p shell, from He 6 to B 10 , calculated within the nuclear shell model. We compare the performance of two leading variational quantum eigensolver algorithms: the unitary coupled cluster (UCC) and the adaptive derivative-assembled pseudo-Trotter (ADAPT) methods, introducing a new metric to quantify the use of quantum resources in each simulation. We find that Slater determinants are the most useful reference states for both approaches. Our analysis suggests that ADAPT is more efficient for nuclei close to magic numbers, while UCC tends to require fewer resources toward the mid shell. This work lays the groundwork for robust benchmarking of quantum algorithms in nuclear structure studies.

arXiv:2507.13819•Physical Review C•Oct 20, 2025•5 citations

Circuit-Efficient Qubit Excitation-Based Variational Quantum Eigensolver

Zhijie Sun, Xiaopeng Li, Jie Liu +2 more

The adaptive derivative-assembled pseudo-trotter (ADAPT) variational quantum eigensolver (VQE) is an appealing framework for iteratively constructing accurate representations of ground- and excited-state wave functions as products of exponentialized one- and two-body operators acting on a reference state. In this work, we propose a CNOT-efficient circuit for implementing exponentialized two-body qubit-excitation-based (QEB) operators, enabling the construction of the low-depth wave function Ansätze. Our proposed circuit architecture employs a 2-qubit-controlled rotation gate flanked by two layers of CNOT gates, requiring only 9 CNOT gates per two-body QEB operator while preserving essential symmetries, including particle number and the Z -component of spin. By integrating these optimized circuits into the ADAPT–VQE framework, we achieve a reduction in circuit depth of approximately 28% compared to the original QEB ADAPT–VQE method, without sacrificing accuracy in simulating ground- and excited-state properties of small molecules. Numerical simulations validate the improved performance of our approach, demonstrating its potential as an efficient tool for quantum simulations of electronic structures.

arXiv:2406.11699•Journal of Chemical Theory and Computation•May 8, 2025•8 citations

Neutron-proton pairing correlations described on quantum computers

Jing Zhang, Denis Lacroix A, Yann Beaujeault-Taudière

The ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) approach is used to solve the neutron-proton pairing problem in atomic nuclei. This variational approach is considered today to be one of the most powerful methods to iteratively find the ground state of a many-body problem, provided a performing set of operators, called the pool of operators, is used to explore the Hilbert space of many-body wave-functions. Three different pools of operators, which might eventually break one or several symmetries of the Hamiltonian during the descent to the ground state, are tested for the neutron-proton pairing problem. We observe that the breaking of some symmetries during the optimization of the trial wave function might, in general, help to speed up the convergence towards the ground state. Still, we rejected the pool of operators that might explicitly break the total particle number because they become uncontrollable during the optimization process. Overall, we observed that the iterative optimization process rapidly becomes a delicate problem when the number of parameters to build the Ansatz increases, and the energy might get stuck at energies higher than the ground state energy. To improve the convergence in this case, several techniques have been proposed, with some better controlling the symmetries during the energy minimization. Among the proposed methods, two have proved effective: one based on an embedding technique and the other on a randomized preparation of the initial state. We conclude that the ADAPT-VQE, complemented by these techniques, can provide a very accurate description of the neutron-proton pairing problem, and can outperform other standardly used techniques that break the particle number symmetry and restore afterwards.

arXiv:2408.17294•Physical Review C•Dec 19, 2024•9 citations

Benchmarking Adaptive Variational Quantum Eigensolvers

Daniel Claudino, Jerimiah Wright, Alexander J. McCaskey +1 more

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

arXiv:2011.01279•Frontiers in Chemistry•Dec 4, 2020•52 citations
Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver (SSVQE) combined with an adaptive derivative-assembles pseudo-trotter (ADAPT) ansatz to obtain the low-lying states of any nuclear system in a single optimization run. As an example, we apply this method in this work to a trivial identical nucleon system, two nucleons in the 0p3/20p_{3/2}0p3/2​ orbital, mapped to 4 qubits depicting m-scheme single-particle states including a surface delta effective interaction using the Jordan-Wigner transformation. The ADAPT-SSVQE algorithm, by utilizing a symmetry-preserving double-excitation ADAPT operator pool, uniquely optimizes a weighted energy sum, forcing the simultaneous convergence of two lowest states within the total angular momentum MJ=0M_J=0MJ​=0 subspace. We demonstrate the accuracy of the method by benchmarking against the exact diagonalization, confirming its potential for probing nuclear structure and pairing phenomena on current and near-future quantum devices without requiring multi-step procedure for excited states.
The nuclear shell model is a general way of expressing the many-body nuclear Hamiltonian and deciphering the underlying nuclear structure. In today's era of modern and high-power computation, the primary limitation of the nuclear shell model is the enormous dimensionality of its Hilbert space, which far exceeds available storage capacity and prevents the diagonalization of the full Hamiltonian matrix in that space. Quantum computing offers a scalable solution to bypass this curse of dimensionality. In this work, we introduce a single-run quantum simulation capable of obtaining multiple shell-model eigenstates simultaneously. The nuclear Hamiltonian is transformed from a bit to a qubit basis using the Jordan-Wigner transformation, explicitly preserving fermionic anti-commutation. We employ a Subspace Search Variational Quantum Eigensolver (SSVQE) along with an Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansatz to construct the quantum circuit required to solve the shell-model problem. The ADAPT-SSVQE algorithm uses a symmetry-preserving single and double-excitation operator pool and optimizes a weighted energy sum to obtain the simultaneous convergence of all eigenstates within a targeted MJ subspace, eliminating the need for post-processing efforts to extract excited spectra. We benchmark this approach by solving the problem for two and three identical nucleons in a j = 9/2 orbital, successfully extracting five and ten mutually orthogonal states, respectively, within a 10-qubit active space. The algorithm achieves spectroscopic accuracy, in simulation, relative to exact diagonalization and intrinsically restores total angular momentum (\hat{J}^2) symmetry.
A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems. The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) towards the ground state of the many-body problem. This method is shown to be accurate with only a small overhead in terms of quantum resources required to get the ground state. We also show that the quantum algorithm might be used to facilitate the convergence of the ADAPT-VQE method itself. Successful applications of the technique are made to like-particle pairing as well as neutron-proton pairing. Finally, the H 4 molecule’s dissociation also illustrates the technique, demonstrating its accuracy and versatility.
Quantum computing is one of the most promising technologies of the near future, and the simulation of quantum many-body systems is a natural application. In this work, we present classical simulations of the ground states of light atomic nuclei within the p shell, from He 6 to B 10 , calculated within the nuclear shell model. We compare the performance of two leading variational quantum eigensolver algorithms: the unitary coupled cluster (UCC) and the adaptive derivative-assembled pseudo-Trotter (ADAPT) methods, introducing a new metric to quantify the use of quantum resources in each simulation. We find that Slater determinants are the most useful reference states for both approaches. Our analysis suggests that ADAPT is more efficient for nuclei close to magic numbers, while UCC tends to require fewer resources toward the mid shell. This work lays the groundwork for robust benchmarking of quantum algorithms in nuclear structure studies.
The adaptive derivative-assembled pseudo-trotter (ADAPT) variational quantum eigensolver (VQE) is an appealing framework for iteratively constructing accurate representations of ground- and excited-state wave functions as products of exponentialized one- and two-body operators acting on a reference state. In this work, we propose a CNOT-efficient circuit for implementing exponentialized two-body qubit-excitation-based (QEB) operators, enabling the construction of the low-depth wave function Ansätze. Our proposed circuit architecture employs a 2-qubit-controlled rotation gate flanked by two layers of CNOT gates, requiring only 9 CNOT gates per two-body QEB operator while preserving essential symmetries, including particle number and the Z -component of spin. By integrating these optimized circuits into the ADAPT–VQE framework, we achieve a reduction in circuit depth of approximately 28% compared to the original QEB ADAPT–VQE method, without sacrificing accuracy in simulating ground- and excited-state properties of small molecules. Numerical simulations validate the improved performance of our approach, demonstrating its potential as an efficient tool for quantum simulations of electronic structures.
The ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) approach is used to solve the neutron-proton pairing problem in atomic nuclei. This variational approach is considered today to be one of the most powerful methods to iteratively find the ground state of a many-body problem, provided a performing set of operators, called the pool of operators, is used to explore the Hilbert space of many-body wave-functions. Three different pools of operators, which might eventually break one or several symmetries of the Hamiltonian during the descent to the ground state, are tested for the neutron-proton pairing problem. We observe that the breaking of some symmetries during the optimization of the trial wave function might, in general, help to speed up the convergence towards the ground state. Still, we rejected the pool of operators that might explicitly break the total particle number because they become uncontrollable during the optimization process. Overall, we observed that the iterative optimization process rapidly becomes a delicate problem when the number of parameters to build the Ansatz increases, and the energy might get stuck at energies higher than the ground state energy. To improve the convergence in this case, several techniques have been proposed, with some better controlling the symmetries during the energy minimization. Among the proposed methods, two have proved effective: one based on an embedding technique and the other on a randomized preparation of the initial state. We conclude that the ADAPT-VQE, complemented by these techniques, can provide a very accurate description of the neutron-proton pairing problem, and can outperform other standardly used techniques that break the particle number symmetry and restore afterwards.
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.