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Annales De L Institut Henri Poincare-physique Theorique

Addendum “Complex transformation method and resonances in one-body quantum systems”

Israel Michael Sigal

Published Jan 1, 1984• 0 citations
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Related papers

Addendum to the N‐body problem in quantum mechanics

Communications on Pure and Applied Mathematics•Jul 1, 1987•2 citations

Quantum computing for atomic and molecular resonances

Teng Bian, Sabre Kais

The complex-scaling method can be used to calculate molecular resonances within the Born–Oppenheimer approximation, assuming that the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second quantization and then used the Jordan–Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the direct measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H2− molecule. The numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.

arXiv:2011.13999•The Journal of Chemical Physics•May 19, 2021•11 citations

Addendum to "Phenomenological Derivation of the Schrodinger Equation"

Fernando Ogiba

Progress in physics•Apr 1, 2014•1 citation

Series expansions in closed and open quantum many-body systems with multiple quasiparticle types

Lea Lenke, Andreas Schellenberger, Kai Phillip Schmidt

The established approach of perturbative continuous unitary transformations (pCUTs) constructs effective quantum many-body Hamiltonians as perturbative series that conserve the number of one quasiparticle type. We extend the pCUT method to similarity transformations---dubbed ${\text{pcst}}^{++}$---allowing for multiple quasiparticle types with complex-valued energies. This enlarges the field of application to closed and open quantum many-body systems with unperturbed operators corresponding to arbitrary superimposed ladder spectra. To this end, a generalized counting operator is combined with the quasiparticle generator for open quantum systems recently introduced by Schmiedinghoff and Uhrig [G. Schmiedinghoff and G. S. Uhrig, SciPost Phys. 13, 122 (2022)]. The ${\text{pcst}}^{++}$ then yields model-independent block-diagonal effective Hamiltonians and Lindbladians, allowing a linked-cluster expansion in the thermodynamic limit similar to the conventional pCUT method. We illustrate the application of the ${\text{pcst}}^{++}$ method by discussing representative closed, open, and non-Hermitian quantum systems.

arXiv:2302.01000•Physical Review A•Jul 31, 2023•9 citations

Quantum defragmentation algorithm

Daniel Klaus Burgarth, Vittorio Giovannetti

In this addendum to our paper [D. Burgarth and V. Giovannetti, Phys. Rev. Lett. 99, 100501 (2007)] we prove that during the transformation that allows one to enforce control by relaxation on a quantum system, the ancillary memory can be kept at a finite size, independently from the fidelity one wants to achieve. The result is obtained by introducing the quantum analog of defragmentation algorithms which are employed for efficiently reorganizing classical information in conventional hard disks.

arXiv:1006.4107•Physical Review A•Aug 19, 2010•1 citation

Resonance overlap in quantum systems

L. E. Reichl, W. A. Lin

Springer eBooks•Apr 6, 2008•0 citations
The complex-scaling method can be used to calculate molecular resonances within the Born–Oppenheimer approximation, assuming that the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second quantization and then used the Jordan–Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the direct measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H2− molecule. The numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.
The established approach of perturbative continuous unitary transformations (pCUTs) constructs effective quantum many-body Hamiltonians as perturbative series that conserve the number of one quasiparticle type. We extend the pCUT method to similarity transformations---dubbed pcst++{\text{pcst}}^{++}pcst++---allowing for multiple quasiparticle types with complex-valued energies. This enlarges the field of application to closed and open quantum many-body systems with unperturbed operators corresponding to arbitrary superimposed ladder spectra. To this end, a generalized counting operator is combined with the quasiparticle generator for open quantum systems recently introduced by Schmiedinghoff and Uhrig [G. Schmiedinghoff and G. S. Uhrig, SciPost Phys. 13, 122 (2022)]. The pcst++{\text{pcst}}^{++}pcst++ then yields model-independent block-diagonal effective Hamiltonians and Lindbladians, allowing a linked-cluster expansion in the thermodynamic limit similar to the conventional pCUT method. We illustrate the application of the pcst++{\text{pcst}}^{++}pcst++ method by discussing representative closed, open, and non-Hermitian quantum systems.