Speaker
Description
Quantum resonances are remarkable phenomena observed across various systems, including atomic nuclei. A well-established theoretical method for calculating resonance properties is complex scaling [1], in which we scale the co-ordinate by a complex phase factor $\theta$ i.e $r \to re^{i\theta}$, transforming the Hamiltonian to $H({r}, \theta) = U(\theta)H(r)U(\theta)^{-1}.$ This widely used method requires a large basis set for accurate predictions of complex energy eigenvalue, leading to significant computational challenges. Quantum computers present a promising avenue to address this complexity. Due to the limitations in qubit count and fidelity, hybrid quantum-classical algorithms, such as the Variational Quantum Eigensolver (VQE), are particularly well-suited for noisy intermediate-scale quantum (NISQ) devices [2,3]. However, VQE cannot be directly applied to resonances due to the non-Hermitian nature of the Hamiltonian. To overcome these obstacles, alternate approaches have been proposed in the literature where they embed the non-Hermitian operator into a higher-dimensional unitary matrix, enabling the use of quantum algorithms for direct computation of both real and imaginary components of resonance energies [4].
In the present work, we propose a more efficient algorithm utilizing the spectrum scanning approach for Variational Quantum Algorithm (VQA) [5] and advance the framework to explore the eigenstates of non-Hermitian operators efficiently on a quantum computer. We demonstrate the efficiency of this approach by calculating the resonances of a schematic potential, which is set as a benchmark and extended to nuclear systems, and the results are validated against the traditional diagonalization techniques. Our findings highlight the potential of quantum computing in advancing nuclear physics research, particularly in leveraging noisy intermediate-scale quantum (NISQ) devices for the study of complex quantum systems.
References
1. N. Moiseyev, et al., Molecular Physics 36, 1613 (1978).
2. P. Siwach, P. Arumugam, Phys. Rev. C 104, 034301 (2021).
3. P. Siwach, P. Arumugam, {Phys. Rev. C 105, 064318 (2022).
4. T. Bian, et al., J. Chem. Phys. 154, 194107 (2021).
5. Xu-Dan Xie, et al., Front. Phys. 19, 41202 (2024).
