Related papers: Quantum Computation of Scattering Amplitudes in Sc…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation. A scattering transform is a deep convolution network computed with a cascade of…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on…
We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for…
Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted…
We use the semiclassical formalism based on singular solutions in complex time to compute scattering rates for multiparticle production at high energies. In a weakly coupled $\lambda \phi^4$ scalar field theory in four dimensions, we…
We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.
We present a new method for computing multi-loop scattering amplitudes in Quantum Field Theory. It extends the Generalized Unitarity method by constraining not only the integrand of the amplitude but also its full integrated form. Our…
We present a pedagogical introduction to a series of quantum computing algorithms for the simulation of classical fluids, with special emphasis on the Carleman-Lattice Boltzmann method.
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…
Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called…
We devise a technique for defining and computing n-point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively-finite…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the…
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which…