Variational Algorithms Model Nuclear Structure on Noisy Quantum Devices.

Variational algorithms successfully model complex nuclear systems, achieving energy and angular momentum predictions consistent with exact diagonalization. Research utilising five increasingly complex cranked Nilsson-Strutinsky models demonstrates variational errors typically below one percent, though slight entropy discrepancies emerge due to numerical precision and ansatz limitations.

The behaviour of atomic nuclei at high rotational speeds presents a significant computational challenge, demanding increasingly sophisticated methods for accurate modelling. Researchers are now applying quantum computing techniques, specifically variational algorithms, to simulate these complex systems, offering a potential pathway to understanding nuclear structure beyond the reach of classical computation. Dhritimalya Roy, from Presidency University, Kolkata, details this approach in a new study entitled ‘Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms’. The work explores the application of the Variational Eigensolver (VQE), a hybrid quantum-classical algorithm, to models based on the cranked Nilsson-Strutinsky (CNS) framework, a theoretical tool used to describe the behaviour of nuclei rotating at high angular velocities. By constructing increasingly complex models and comparing results obtained via VQE with those from exact diagonalization, a precise but computationally intensive classical method, the study assesses the viability of utilising near-term quantum devices for simulating rotational nuclear structure and provides insights into the limitations and potential of this emerging field.

Recent advances in quantum computing are enabling the development of novel algorithms to address complex problems in nuclear physics, particularly in understanding the structure and dynamics of atomic nuclei. Variational algorithms, such as the Variational Eigensolver (VQE), are emerging as promising candidates for simulating many-body systems on near-term quantum devices, offering a potential route to overcome the limitations of classical computational methods. This work details an investigation into the application of VQE to schematic model simulations, building upon the well-established cranked Nilsson-Strutinsky (CNS) framework to gain insights into the behaviour of deformed nuclei undergoing rapid rotation, a phenomenon crucial for understanding the properties of exotic nuclei far from stability. The aim is to demonstrate the feasibility and accuracy of VQE in predicting key observables, paving the way for more sophisticated simulations of realistic nuclear systems.

The CNS model provides a mean-field description of nuclei, incorporating single-particle energies, pairing interactions, and the effects of rotation, offering a valuable framework for understanding the collective behaviour of nucleons. However, solving the CNS equations for complex nuclei often demands significant computational resources, limiting the scope of investigations. Five increasingly complex CNS-like models were constructed, systematically increasing the level of sophistication to assess VQE’s performance as complexity grows. These models incorporate single-particle level spacings, pairing correlations, cranking terms representing rotation, and particle-number conservation, a fundamental requirement for realistic nuclear simulations. This systematic approach allows evaluation of VQE’s scalability and accuracy as it tackles increasingly challenging problems, isolating the effects of different physical phenomena and assessing the algorithm’s ability to capture them accurately.

To implement VQE, the Hamiltonian of each CNS-like model was mapped onto a set of qubits, representing the degrees of freedom of the nucleons, enabling simulation on a quantum computer. This mapping requires careful consideration of the encoding scheme and the choice of qubit operators to represent the various terms in the Hamiltonian, ensuring the quantum simulation accurately reflects the underlying physics. A classical-quantum hybrid procedure was then employed, iteratively optimising the parameters of a variational ansatz on a classical computer while evaluating the energy expectation value on a quantum computer, leveraging the strengths of both classical and quantum computation. This hybrid approach efficiently explores the vast parameter space of the variational ansatz, minimising the energy and obtaining approximate solutions.

To validate the VQE results, they were compared with those obtained using exact diagonalization, a highly accurate but computationally demanding method. Good agreement was observed in the calculated energy eigenvalues and wavefunctions, validating VQE’s potential as a viable method for simulating nuclear structure. This agreement confirms that VQE can accurately capture the essential physics of the CNS-like models, providing confidence in its ability to tackle more complex systems.

Notably, slight variances were observed in the calculated entropy values between the exact diagonalization and VQE results, attributed to limitations in numerical precision and the expressivity of the chosen variational ansatz. Entropy, a measure of the system’s disorder or uncertainty, is particularly sensitive to the details of the wavefunction and requires a highly expressive ansatz to capture accurately. The variational ansatz, a trial wavefunction used in VQE, has a limited ability to represent the full complexity of the many-body wavefunction, leading to inaccuracies in the calculated entropy. Improving the expressivity of the ansatz, by incorporating more variational parameters and more complex functional forms, is crucial for achieving higher accuracy.

These findings pave the way for applying variational algorithms to investigate larger and more realistic CNS-type systems, currently intractable for classical computational methods. The ability to accurately simulate these systems would provide valuable insights into the structure and dynamics of exotic nuclei, helping to understand the limits of nuclear stability and the origin of the elements. Future research will focus on developing more expressive variational ansätze, improving the efficiency of the optimisation algorithms, and exploring the use of more advanced quantum hardware. The development of fault-tolerant quantum computers will be crucial for tackling even more complex problems in nuclear physics, opening up new avenues for scientific discovery.

In conclusion, this work demonstrates the feasibility and accuracy of VQE in simulating nuclear structure, providing a promising pathway for tackling complex problems in nuclear physics on near-term quantum devices. The systematic comparison with exact diagonalization validates VQE’s potential as a viable method for simulating nuclear systems, paving the way for future research on more complex and realistic models. The observed discrepancies in the calculated entropy highlight the importance of carefully selecting the variational ansatz and optimising its parameters to ensure accurate results. The development of more expressive variational ansätze and the use of more advanced quantum hardware will be crucial for unlocking the full potential of VQE and tackling even more challenging problems in nuclear physics.