We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant states of α − α system and achieve results in good agreement with traditional methods. Our study offers a new perspective on calculating eigenvalues of non-Hermitian operators and lays some groundwork for further exploration of nuclear resonances using quantum computing.
We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant states of α − α system and achieve results in good agreement with traditional methods. Our study offers a new perspective on calculating eigenvalues of non-Hermitian operators and lays some groundwork for further exploration of nuclear resonances using quantum computing.
By using the quantum computing the properties of hypernuclei Λ5He, ΛΛ6He and Λ9Be can be investigated within microscopic cluster model. Our approach combines quantum neural network (QNN) with iterative Harrow-Hassidim-Lloyd (IHHL) algorithm (abbreviated as QNN-IHHL) to solve the quantum many-body problem. To efficiently describe resonance phenomena, we employ complex scaling and eigenvector continuation techniques, providing a robust framework for identifying few-cluster resonance parameters within quantum computing. To validate our quantum algorithm, the resonant 4+ state of Λ9Be is chosen as a core example. With QNN-IHHL algorithm we realize a fully quantum workflow, which provides a novel framework and some ground work for exploring resonance properties in complex nuclear many-body systems.
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling, standard quantum computing cannot solve for complex eigenvalues directly. Therefore, it is necessary to embed the non-Hermitian operator into a larger dimensional unitary operator. Additionally, for the case of two basis vectors, we improve the traditional direct measurement method and optimize the quantum circuit. Ultimately, using the α + α system as an example, we obtain the complex eigenenergies from the quantum computer that are consistent with those obtained from direct Hamiltonian diagonalization.
Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (nonunitary) linearized coupled cluster theory, where the term ``light molecular systems'' refers to those molecules whose constituent atoms have low atomic number. For the purposes of practical computations, we make suitable changes to the HHL framework. This entails two aspects: (1) Adapt, prescribing a novel scaling approach that allows one to scale any arbitrary Hermitian matrix, A, that in turn dictates the controlled-rotation angles without having to precompute the eigenvalues of A, and yet achieve a reasonably high precision in $|x\ensuremath{\rangle}$, and (2) Lite, for which we devise techniques that reduce the depth of the relevant quantum circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing: AdaptHHLite in its appropriate forms for noisy intermediate-scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource lean, using simulation as well as the 11-qubit IonQ quantum hardware.
We propose an iterative improvement method for the Harrow-Hassidim-Lloyd (HHL) algorithm to solve a linear system of equations. This is a quantum-classical hybrid algorithm. The accuracy is essential to solve the linear system of equations. However, the accuracy of the HHL algorithm is limited by the number of quantum bits used to express the eigenvalues of the matrix. Our iterative method improves the accuracy of the HHL solutions, and gives higher accuracy which surpasses the accuracy limited by the number of quantum bits. In practical HHL algorithm, a huge number of measurements is required to obtain good accuracy, even if we provide a sufficient number of quantum bits for the eigenvalue expression, since the solution is statistically processed from the measurements. Our improved iterative method can reduce the number of measurements. Moreover, the sign information for each eigenstate of the solution is lost once the measurement is made, although the sign is significant. Therefore, the naïve iterative method of the HHL algorithm may slow down, especially, when the solution includes wrong signs. In this paper, we propose and evaluate an improved iterative method for the HHL algorithm that is robust against the sign information loss, in terms of the number of iterations and the computational accuracy.
Quantum computing is a potential approach for addressing computational challenges in solving electromagnetic problems. A quantum method, called the Harrow/Hassidim /Lloyd (HHL) algorithm has recently been applied to solve the equations from finite-element-method (FEM) formulation of electromagnetic problems. Here we address a further step in this direction. Since quantum state vectors always have unit norm, the solution vector from HHL is only proportional to the final electromagnetic solutions. The magnitude of the final electromagnetic solution vector remains unavailable from HHL In this paper, a new quantum formulation is proposed to find the magnitude of the final electromagnetic solutions. The proposed method can be used to scale the HHL results to the correct magnitude of electromagnetic solutions. In this way, the proposed method is a further advance in making the quantum computing more effective in solving electromagnetic problems.
Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (non-unitary) linearised coupled cluster theory. We alter the HHL algorithm to integrate two novel aspects- (a) we prescribe a novel scaling approach that allows one to scale any arbitrary symmetric positive definite matrix A, to solve for Ax = b and achieve x with reasonable precision, all the while without having to compute the eigenvalues of A, and (b) we devise techniques that reduce the depth of the overall circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing- AdaptHHLite in its appropriate forms for noisy intermediate scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource-lean, using simulation as well as the 11-qubit IonQ quantum hardware.