On a rudimentary many-electron model

L. C. M. Miranda, D. ter Haar

Michel Talagrand

We give a brief and basic introduction to perturbation theory. The main idea is to attempt to consider the situation of interest as a small perturbation of a simpler situation (which can be understood completely), and in particular to consider a system with a weak interaction as a perturbation of a non-interacting system. We develop the interaction picture, which allows approximating the time-evolution of an interacting system by the partial sums of the Dyson series, a fundamental tool for the sequel. We illustrate these ideas on a rudimentary model of the interaction of electrons and “photons”.

S. Raimes

Oliver Knitter

Neural-network quantum states (NQS) is an exciting area of quantum-inspired machine learning, wherein a fully classical neural network is used to efficiently learn the optimal state vector for a quantum unsupervised learning problem, bypassing the need to model the full Hilbert space, which is exponentially large. In theory, NQS architectures are broadly applicable, and have been demonstrated successfully on several fundamental applications. We seek to further explore the practical utility of NQS as a black box solver for various applications in the scientific computing domain. We first present NQS as an explicit avenue for de-quantizing variational quantum eigensolvers, demonstrating with the variational quantum linear solver (VQLS). We then explore the utility of VQLS and its de-quantization, VNLS, as black box matrix inversion tools for a Newton-based linear complementarity solver, used to model the time evolution of a rudimentary granular medium. Turning our attention toward applications of NQS in quantum chemistry, we introduce a new retentive network (RetNet) autoregressive NQS ansatz to solve electronic ground state problems, and explore the incorporation of neural annealing techniques to these problems as a means of improving accuracy and ease of training. We finish with a rudimentary scaling law analysis of the RetNet architecture and its immediate autoregressive predecessors as applied to electronic structure calculations.

Eric Robert Morgan

abstract: In this paper, optimal control routines are applied to an existing problem of electron state transfer to determine if spin information can successfully be moved across a chain of donor atoms in silicon. The additional spin degrees of freedom are introduced into the formulation of the problem as well as the control optimization algorithm. We find a timescale of transfer for spin quantum information across the chain fitting with a t > π/A and t > 2π/A transfer pulse time corresponding with rotation of states on the electron Bloch sphere where A is the electron-nuclear coupling constant. Introduction of a magnetic field weakens transfer\nefficiencies at high field strengths and prohibits anti-aligned nuclear states from transferring. We also develop a rudimentary theoretical model based on simulated results and partially validate the characteristic transfer times for spin states. This model also establishes a framework for future work including the introduction of a magnetic field.