The Non-Equilibrium Green's Function (NEGF) is the standard formalism for nano-scale electron transport. By recasting the NEGF scattering problem as a linear system of equations whose solution encodes the transmission and reflection amplitudes, we present the first quantum computerized implementation of NEGF. We apply both the Harrow--Hassidim--Lloyd and Variational Quantum Linear Solver algorithms to compute the transmission coefficient $T(E)$ of quantum dragon nanodevices within the single-band tight-binding model. Quantum dragon devices exhibit perfect transmission across the full conducting band regardless of internal disorder. The problem maps onto compact circuits of 3 and 4 total physical qubits for the 2-site and 6-site dragon devices, respectively. A similarity transformation block-diagonalizes the NEGF linear system reducing the Pauli decomposition of the block-encoded matrix. We demonstrate the feasibility of quantum computation by performing ideal and noise-aware simulations and computations on physical IBM quantum processor.
The Non-Equilibrium Green's Function (NEGF) is the standard formalism for nano-scale electron transport. By recasting the NEGF scattering problem as a linear system of equations whose solution encodes the transmission and reflection amplitudes, we present the first quantum computerized implementation of NEGF. We apply both the Harrow--Hassidim--Lloyd and Variational Quantum Linear Solver algorithms to compute the transmission coefficient T(E) of quantum dragon nanodevices within the single-band tight-binding model. Quantum dragon devices exhibit perfect transmission across the full conducting band regardless of internal disorder. The problem maps onto compact circuits of 3 and 4 total physical qubits for the 2-site and 6-site dragon devices, respectively. A similarity transformation block-diagonalizes the NEGF linear system reducing the Pauli decomposition of the block-encoded matrix. We demonstrate the feasibility of quantum computation by performing ideal and noise-aware simulations and computations on physical IBM quantum processor.
As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green’s function (NEGF) formalism is a widely used method for simulating quantum transport in semiconductor devices, but it is computationally demanding. Quantum computing offers a promising solution, in this work, we pioneer the application of the variational quantum linear solver (VQLS) to the NEGF problem, addressing the challenges associated with handling complex numbers inherent in quantum transport equations. We introduce a new cost function tailored to this framework, demonstrating improved performance over existing approaches. Furthermore, we show that VQLS can efficiently parallelize the computation across different energy levels, significantly reducing computational costs. Our results highlight the potential of variational quantum algorithms (VQAs) in enhancing the scalability and efficiency of quantum transport simulations.
With the technical progress of radio-frequency setups, high frequency quantum transport experiments have moved from theory to the lab. So far the standard theoretical approach used to treat such problems numerically - known as Keldysh or NEGF (Non Equilibrium Green's Functions) formalism - has not been very successful mainly because of a prohibitive computational cost. We propose a reformulation of the non-equilibrium Green's function technique in terms of the electronic wave functions of the system in an energy-time representation. The numerical algorithm we obtain scales now linearly with the simulated time and the volume of the system, and makes simulation of systems with 105-106atoms/sites feasible. We illustrate our method with the propagation and spreading of a charge pulse in the quantum Hall regime. We identify a classical and a quantum regime for the spreading, depending on the number of particles contained in the pulse. This numerical experiment is the condensed matter analogue to the spreading of a Gaussian wavepacket discussed in quantum mechanics textbooks.
This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor device simulations focuses on solving the Poisson equation, where the coefficient matrix of the sparse linear system is real and symmetric. Solving the quantum transport equation, however, leads to coefficient matrices that are complex and non-symmetric. This work addresses the challenges of applying VQLS to quantum transport simulations. We propose new forms of cost functions to solve complex and non-symmetric linear systems with faster computing speed. We further develop efficient decomposition methods for cost function evaluation, which target reducing the quantum circuit complexity and improving noise robustness when solving the quantum transport equation using the nonequilibrium Green's function method. While classical computation faces the challenge of the “curse of dimensionality” as the spatial-energy numerical grid dimensions grow, the proposed quantum-computing-based method scales logarithmically with the grid size, which offers a promising opportunity for addressing the computational challenges of solving quantum transport in semiconductor devices.
We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes.
Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.
Abstract We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green’s function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive—encompassing pump–probe scenarios as well as driven quantum systems—we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron–phonon couplings, topological superconductors, and optically responsive molecular junctions where electron–photon couplings are relevant.
Real-time nonequilibrium Green functions (NEGFs) have been very successfully used to simulate the dynamics of correlated many-particle systems far from equilibrium. However, NEGF simulations are computationally expensive since the effort scales cubically with the simulation duration. Recently, we introduced the G1--G2 scheme that allows for a dramatic reduction to time-linear scaling [N. Schl\"unzen et al., Phys. Rev. Lett. 124, 076601 (2020); J.-P. Joost et al., Phys. Rev. B 101, 245101 (2020)]. Here we tackle another problem: the rapid growth of the computational effort with the system size. In many situations where the system of interest is coupled to a bath, to electric contacts, or to similar macroscopic systems for which a microscopic resolution of the electronic properties is not necessary, efficient simplifications are possible. This is achieved by the introduction of an embedding self-energy---a concept that has been successful in standard NEGF simulations. Here, we demonstrate how the embedding concept can be introduced into the G1--G2 scheme, allowing us to drastically accelerate NEGF embedding simulations. The approach is compatible with all advanced self-energies that can be represented by the G1--G2 scheme [as described in J.-P. Joost et al., Phys. Rev. B 105, 165155 (2022)] and retains the memoryless structure of the equations and their time-linear scaling. As a numerical illustration, we investigate the charge transfer between a Hubbard nanocluster and an additional site which is of relevance for the neutralization of ions in matter.