Quasiparticle Pairing Encoding Achieves 3 Orders of Magnitude Advantage in Quantum Annealing for Semimagic Nuclei

Understanding the structure of atomic nuclei presents a significant challenge for modern physics, but researchers are now exploring the potential of quantum computing to unlock new insights. Emanuele Costa, Axel Pérez-Obiol, and Javier Menéndez, from the Universitat de Barcelona, along with colleagues including Arnau Rios and Artur García-Sáez, demonstrate a novel encoding scheme that dramatically simplifies the process of representing nuclear properties on a quantum computer. This method, based on pairing nucleon modes, reduces the computational demands of simulating nuclei, achieving a remarkable three orders of magnitude improvement in efficiency compared to conventional techniques. The team’s work opens exciting possibilities for simulating complex nuclear structures using quantum computers, potentially advancing both fundamental understanding and applications in areas like nuclear astrophysics and materials science.

Nuclear Shell Model for Quantum Computation

This body of work explores the application of quantum computing to understand the structure of atomic nuclei, focusing on the nuclear shell model. The research investigates methods for accurately representing the complex interactions within nuclei on quantum computers, a challenge due to the exponential growth of computational demands with increasing nuclear size. A central theme is the development of effective interactions, which simplify calculations while maintaining accuracy in predicting nuclear properties, and the use of many-body perturbation theory to refine these calculations. Researchers are also exploring how nuclei exhibit different shapes and how these shapes influence their behavior.

A growing area of interest is leveraging quantum computers to solve problems in nuclear structure that are intractable for classical computers. This involves mapping the nuclear Hamiltonian onto quantum algorithms like the variational quantum eigensolver. Trapped-ion quantum computers are receiving particular attention as a promising platform for these calculations. This convergence of theoretical approaches and computational power promises a deeper understanding of nuclear structure.

Hardcore Bosons Simulate Nuclear Structure Accurately

Researchers have developed a novel method for simulating nuclear structure using quantum computing, addressing the significant computational cost typically associated with encoding fermionic operators. The study pioneers a full-hardcore boson mapping to represent protons and neutrons, substantially reducing the quantum computational demands of algorithms used to determine nuclear ground states. This approach encodes the nuclear Hamiltonian in terms of quasiparticles constructed from paired nucleon modes possessing opposite magnetic quantum numbers, effectively transforming fermionic behavior into hardcore boson statistics directly mappable onto qubits. The team systematically analyzed medium-mass nuclei to verify that the resulting effective Hamiltonian accurately reproduces known nuclear ground-state properties. This involved constructing a nuclear shell model Hamiltonian, expressed as a sum of single-particle energies and two-body interactions. Researchers then applied this encoding scheme to a trotterized adiabatic evolution, a quantum algorithm used to find the ground state of a system, and demonstrated a computational advantage, revealing a reduction in CNOT gate count of up to three orders of magnitude when compared to the standard Jordan-Wigner encoding.

Boson Mapping Simplifies Nuclear Structure Simulation

Researchers have developed a novel method for simulating nuclear structure using quantum computing, significantly reducing computational demands through an innovative encoding scheme. This approach encodes the nuclear Hamiltonian in terms of quasiparticles constructed from paired nucleon modes, effectively transforming the problem into one involving hardcore bosons, which simplifies the mapping onto qubits. This encoding maintains high accuracy in calculating the ground states of semimagic nuclei across the sd and pf shells, as well as for tin isotopes, while also proving effective for open-shell nuclei. The team systematically analyzed medium-mass nuclei to confirm that the resulting effective Hamiltonian accurately captures nuclear ground-state properties.

A key achievement is the substantial reduction in computational overhead when applied to a trotterized adiabatic evolution. Measurements demonstrate a computational advantage of up to three orders of magnitude in CNOT gate count compared to the standard Jordan-Wigner encoding. The researchers constructed a nuclear shell model Hamiltonian and encoded it using quasiparticles formed from paired nucleon modes, ensuring these quasiparticles obey hardcore boson statistics.

Nuclear Structure Simulation With Reduced Complexity

This research presents a novel method for encoding nuclear systems on quantum computers, significantly reducing the computational complexity typically associated with simulating nuclear structure. By mapping nucleon modes into quasiparticle pairs, the team constructed a projected quasiparticle Hamiltonian that accurately approximates the ground state of semimagic nuclei across several shells and for tin isotopes. Results demonstrate high fidelity and low energy error, achieving a reduction of up to three orders of magnitude in the number of CNOT gates required for computation. The approach proves particularly effective for semimagic nuclei and exhibits comparable performance for lighter oxygen and heavier tin isotopes, suggesting a promising pathway toward efficient simulations of medium- to heavy-mass nuclei.

However, the accuracy of the method diminishes when applied to general open-shell nuclei. To address this limitation, the researchers plan to explore hybrid representations combining fermionic and quasiparticle bases, or to incorporate perturbative corrections to the quasiparticle Hamiltonian. Overall, this work offers a valuable advancement in quantum nuclear physics, balancing computational savings with the need for accurate simulations.