Training Quantum Dragons

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.