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arXiv:2210.08757

A Quantum Algorithm for the Linear Response of Nuclei

Abhishek, Nifeeya Singh, Pooja Siwach, P. Arumugam

Published Oct 17, 2022• 0 citations
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Abstract

We present a quantum algorithm to obtain the response of the atomic nucleus to a small external electromagnetic perturbation. The Hamiltonian of the system is presented by a harmonic oscillator, and the linear combination of unitaries (LCU) based method is utilized to simulate the Hamiltonian on the quantum computer. The output of the Hamiltonian simulation is utilized in calculating the dipole response with the SWAP test algorithm. The results of the response function computed using the quantum algorithm are compared with the experimental data and provide a good agreement. We show the results for $^{120}$Sn and $^{208}$Pb to corroborate with the experimental data in Sn and Pb region and also compare the results with those obtained using the conventional linear response theory.

DOI
10.48550/arxiv.2210.08757

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We present a quantum algorithm to obtain the response of the atomic nucleus to a small external electromagnetic perturbation. The Hamiltonian of the system is presented by a harmonic oscillator, and the linear combination of unitaries (LCU) based method is utilized to simulate the Hamiltonian on the quantum computer. The output of the Hamiltonian simulation is utilized in calculating the dipole response with the SWAP test algorithm. The results of the response function computed using the quantum algorithm are compared with the experimental data and provide a good agreement. We show the results for 120^{120}120Sn and 208^{208}208Pb to corroborate with the experimental data in Sn and Pb region and also compare the results with those obtained using the conventional linear response theory.
It presents a quantum algorithm for efficiently computing the response of an atomic nucleus to a small external electromagnetic perturbation. Specifically, the system's Hamiltonian is modeled as a harmonic oscillator, and the linear combination of unitaries (LCU) approach is employed to simulate the Hamiltonian on a quantum computer. We use the SWAP test to compute the dipole response for 120 Sn and find excellent agreement between the quantum algorithm results and experimental data, compared to conventional linear response theory. Overall, our approach presents a promising advancement in the field of quantum computing and may have significant implications for studying the response of complex physical systems to external perturbations.
The dynamic linear response of a quantum system is critical for understanding both the structure and dynamics of strongly interacting quantum systems, including neutron scattering from materials, photon and electron scattering from atomic systems, and electron and neutrino scattering by nuclei. We present a general algorithm for universal quantum computers to calculate the dynamic linear response function with controlled errors and to obtain information about specific final states that can be directly compared to experimental observations.
We present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilize the Hadamard test and the linear combination of unitaries based methods to compute the expectation values. We apply these methods to calculate the electric quadrupole moment of the deuteron. The results are compared for the Jordan-Wigner transformation and Gray code encoding. We discuss the versatility of our approach that can be utilized in general to calculate several observables on a quantum computer.
We present calculations of nuclear shielding constants, a key ingredient in nuclear magnetic resonance spectroscopy, within a quantum-computing-suitable framework. We employ quantum linear response (qLR) theory in combination with the unitary coupled cluster (UCC) ansatz and its orbital-optimized (oo-UCC), factorized (fUCC), and orbital-optimized factorized (oo-fUCC) variants. The methods are assessed for seven small molecules against CASCI, CASSCF, CCSD, and CCSD(T) reference calculations. The different UCC-based qLR approaches yield shielding constants in good agreement with comparable classical methods. Factorization, which is necessary for quantum-computing implementations, has only a negligible effect on the calculated shielding constants. Orbital optimization, in contrast, leads to substantial improvements, with oo-UCC and oo-fUCC showing markedly better agreement with CCSD and CCSD(T). Our results establish oo-fUCC combined with qLR as a promising approach for computing nuclear shielding constants on quantum computers.
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm.