Technology computer-aided design (TCAD) of semiconductor devices relies on the numerical solution of differential equations in devices. Recent advances in quantum computing provide a new opportunity for TCAD simulations to be performed on a quantum computer. Based on a variational quantum algorithm, we develop a quantum-computing-based method to solve quantum confinement problems in semiconductor nanostructures. As the number of numerical discretization grid points for solving the Schrödinger equation increases, the number of qubits needed scales only logarithmically, ~ ${O}[\log(N)]$ . The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.Technology computer-aided design (TCAD) of semiconductor devices relies on the numerical solution of differential equations in devices. Recent advances in quantum computing provide a new opportunity for TCAD simulations to be performed on a quantum computer. Based on a variational quantum algorithm, we develop a quantum-computing-based method to solve quantum confinement problems in semiconductor nanostructures. As the number of numerical discretization grid points for solving the Schrödinger equation increases, the number of qubits needed scales only logarithmically, ~${O}[\log(N)]$. The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.

IEEE Transactions on Electron DevicesJan 11, 202310 citations

Geometry induced entanglement transitions in nanostructures

J. P. Coe, S. Abdullah, Irene D’Amico

We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.

arXiv:1003.3781Journal of Applied PhysicsApr 21, 20103 citations

Classical Computation in Quantum Nanostructures: A Long Road to an Uncertain Future

D. M. Eigler

Bulletin of the American Physical SocietyMar 10, 20080 citations

Controlling quantum interference in nanostructures

Ali A. Kamli, Smail B. Bougouffa

Physica E Low-dimensional Systems and NanostructuresApr 1, 20030 citations

Theory of a peristaltic pump for fermionic quantum fluids

Francesco Romeo, R. Citro

Motivated by the recent developments in fermionic cold atoms and in nanostructured systems, we propose the model of a peristaltic quantum pump. Differently from the Thouless paradigm, a peristaltic pump is a quantum device that generates a particle flux as the effect of a sliding finite-size microlattice. A one-dimensional tight-binding Hamiltonian model of this quantum machine is formulated and analyzed within a lattice Green's function formalism on the Keldysh contour. The pump observables, as, e.g., the pumped particles per cycle, are studied as a function of the pumping frequency, the width of the pumping potential, the particles mean free path, and system temperature. The proposed analysis applies to arbitrary peristaltic potentials acting on fermionic quantum fluids confined to one dimension. These confinement conditions can be realized in nanostructured systems or, in a more controllable way, in cold atoms experiments. In view of the validation of the theoretical results, we describe the outcomes of the model considering a fermionic cold atoms system as a paradigmatic example.Motivated by the recent developments in fermionic cold atoms and in nanostructured systems, we propose the model of a peristaltic quantum pump. Differently from the Thouless paradigm, a peristaltic pump is a quantum device that generates a particle flux as the effect of a sliding finite-size microlattice. A one-dimensional tight-binding Hamiltonian model of this quantum machine is formulated and analyzed within a lattice Green's function formalism on the Keldysh contour. The pump observables, as, e.g., the pumped particles per cycle, are studied as a function of the pumping frequency, the width of the pumping potential, the particles mean free path, and system temperature. The proposed analysis applies to arbitrary peristaltic potentials acting on fermionic quantum fluids confined to one dimension. These confinement conditions can be realized in nanostructured systems or, in a more controllable way, in cold atoms experiments. In view of the validation of the theoretical results, we describe the outcomes of the model considering a fermionic cold atoms system as a paradigmatic example.

arXiv:1712.05398Physical review. B./Physical review. BMay 29, 20182 citations

{O}[\log(N)]

. The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.