Quantum Annealing Tackles Complex Nuclear Physics Calculations

Scientists have developed a new hybrid quantum-classical algorithm to solve large-scale eigenvalue problems, a crucial requirement in nuclear many-body theory where Hamiltonian matrices often reach exceptionally large dimensions. The method combines quantum annealing and classical deflation to iteratively determine the complete eigenspectrum of both standard and generalised eigenvalue problems. This approach was benchmarked using problems originating from the Equation of Motion Phonon Method, performing calculations on actual quantum hardware and illuminating both the potential and current limitations of near-term quantum devices for tackling complex nuclear physics calculations.

Hybrid quantum-classical deflation extracts complete eigenspectra for nuclear structure modelling

A significant performance boost is achieved with a hybrid quantum-classical algorithm, attaining machine-precision accuracy on eigenvalue calculations within approximately 30 iterations. Classical Simulated Annealing often failed to converge or required over 450 iterations for comparable results, highlighting a clear advantage. This breakthrough addresses a key limitation in nuclear physics, where solving large eigenvalue problems, essential for modelling atomic nuclei, was previously hampered by the coherence and error correction demands of algorithms like Quantum Phase Estimation. The computational complexity of these problems scales rapidly with the number of nucleons within the nucleus, quickly exceeding the capabilities of even the most powerful classical supercomputers. Traditional methods struggle to accurately determine the energy levels and wavefunctions of these complex systems. This hinders our understanding of nuclear structure and reactions.

Dr. James Maxwell and colleagues successfully extracted complete eigenspectra from problems originating from the Equation of Motion Phonon Method, utilising actual quantum hardware for the first time and demonstrating a novel computational pathway. Large-scale eigenvalue problems are commonplace in nuclear many-body theory, with Hamiltonian matrices often becoming extremely large. For instance, matrices with dimensions exceeding 1000×1000 are not uncommon in realistic nuclear structure calculations. Quantum computing presents new approaches to tackle these demanding problems, but the Quantum Phase Estimation algorithm, while theoretically powerful, requires levels of coherence and error correction beyond current quantum hardware capabilities. Maintaining quantum coherence, the superposition of quantum states, for sufficiently long periods is a major technological hurdle, as even minor environmental disturbances can cause decoherence and introduce errors into the calculation.

A practical near-term strategy involves using quantum annealing, which reformulates eigenvalue problems into quadratic unconstrained binary optimisation formulations suitable for existing processors. Quantum annealers, such as those produced by D-Wave Systems, are designed to find the minimum energy state of a given system, effectively solving optimisation problems. The team proposed a hybrid quantum-classical algorithm combining quantum annealing and classical deflation to iteratively determine the complete eigenspectrum of both standard and generalised eigenvalue problems. Classical deflation is a technique used to reduce the size of the eigenvalue problem by successively removing the contributions of already-known eigenvalues, thereby simplifying the remaining calculations. Calculations performed on actual quantum hardware benchmarked this method, demonstrating both its capabilities and limitations when applied to nuclear eigenvalue problems. The choice of the Equation of Motion Phonon Method as a benchmark is significant, as it is a widely used technique for describing collective excitations in nuclei, such as vibrations and rotations.

For the largest matrix size tested, classical Simulated Annealing required approximately 450 iterations to reach an eigenvalue accuracy of 10−8. In contrast, the hybrid method attained the same accuracy in around 30 iterations, consistently exceeding the performance of classical methods across different multipolarities and matrix dimensions. Multipolarity refers to the angular momentum of the collective excitation, and varying this parameter allows for a comprehensive assessment of the algorithm’s performance. This work illustrates the potential for applying the method to larger and more complex nuclear models, providing a means to explore limitations and refine the algorithm’s parameters. Future investigation will concentrate on the effects of noise and qubit connectivity on calculation accuracy and efficiency, alongside exploring alternative deflation strategies to further improve performance. Qubit connectivity refers to the physical connections between qubits on the quantum processor, and limited connectivity can restrict the types of problems that can be efficiently solved.

Hybrid quantum-classical methods enable near-term exploration of nuclear structure

Nuclear physicists routinely confront the challenge of modelling atomic nuclei, requiring solutions to extraordinarily complex eigenvalue problems that describe the allowed energy levels within the nucleus itself. These energy levels dictate the stability and decay properties of the nucleus, and accurate calculations are essential for understanding nuclear reactions in stars and other astrophysical environments. While the Quantum Phase Estimation algorithm promises a systematic approach, its demands for stable quantum bits currently exceed the capabilities of available hardware. This research offers a pragmatic alternative, utilising quantum annealing, but relies on classical deflation techniques to progressively refine the results. The iterative nature of the hybrid approach allows for the gradual improvement of the solution, leveraging the strengths of both quantum and classical computation.

Acknowledging that fully coherent quantum computers remain a distant prospect, this hybrid approach offers a valuable pathway for utilising existing, albeit imperfect, quantum hardware. It allows nuclear physicists to begin exploring complex nuclear models on real quantum annealers and gaining insights unattainable through purely classical methods. The team successfully demonstrated a hybrid quantum-classical algorithm capable of extracting complete eigenspectra from eigenvalue problems. Eigenspectra represent the set of characteristic solutions for a given system. Performing calculations on a D-Wave quantum annealer using data from the Equation of Motion Phonon Method validated the approach and highlighted the potential for tackling previously intractable nuclear physics calculations, potentially leading to a deeper understanding of the fundamental forces governing matter. The ability to accurately calculate eigenspectra is fundamental to predicting nuclear properties and understanding the behaviour of matter under extreme conditions, such as those found in neutron stars and supernovae.

The researchers successfully demonstrated a hybrid quantum-classical algorithm for calculating the complete eigenspectra of eigenvalue problems. This is important because accurately determining these spectra is crucial for modelling atomic nuclei and understanding nuclear reactions. By combining quantum annealing with classical deflation techniques, the method allows for the analysis of complex nuclear models on existing D-Wave quantum hardware. The team validated their approach using data from the Equation of Motion Phonon Method, illustrating the capabilities and limitations of near-term quantum devices in nuclear physics.