Faster spectral density calculation using energy moments

Abstract

Accurate predictions of inclusive scattering cross sections in the linear response regime require efficient and controllable methods to calculate the spectral density in a strongly-correlated many-body system. In this work we reformulate the recently proposed Gaussian Integral Transform technique in terms of Fourier moments of the system Hamiltonian which can be computed efficiently on a quantum computer. One of the main advantages of this framework is that it allows for an important reduction of the computational cost by exploiting previous knowledge about the energy moments of the spectral density. For a simple model of medium mass nucleus like ${}^{40}$Ca and target energy resolution of $1$ MeV we find an expected speed-up of $\approx 125$ times for the calculation of the giant dipole response and of $\approx 50$ times for the simulation of quasi-elastic electron scattering at typical momentum transfers.

13 pages, 4 figures

References in corpus (12)

• The Kernel Polynomial Method
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon-nucleon interactions
• Error mitigation via verified phase estimation
• Ab initio computation of the longitudinal response function in ${}^{40}$Ca
• Fast-forwarding quantum evolution
• Machine learning-based inversion of nuclear responses
• Spectral density reconstruction with Chebyshev polynomials
• On the ill-posed character of the Lorentz integral transform
• Spectral function for ${}^4$He using the Chebyshev expansion in coupled-cluster theory

Cited by in corpus (4)

• Quantum error mitigation for Fourier moment computation
• Calculating the many-body density of states on a digital quantum computer
• Channel-based framework for phase esimation of multiple eigenvalues
• Quantum Simulation of Nuclear Dynamics in First Quantization