Transforming the Computational Workhorse of Electronic Structure

Alexander F. Kemper

Rowan Brad Quni-Gudzinas

The electron is the most precisely measured particle in physics and the workhorse of modern computation, yet the theoretical structure in which it lives rests on assumptions that are load-bearing but rarely interrogated: the complex Hilbert-space postulate, the spin-statistics theorem's premises, the Archimedean valuation of every measured quantity, the thermodynamic foundations of irreversible computation, and the identification of the electron itself as a fixed elementary object rather than a vacuum- and environment-dependent excitation. This Full Edition expands the v0.1 architecture into the treatise proper: nine parts and fifty-one chapters, each load-bearing assumption audited by a fixed six-step procedure.

Manas Sajjan, Shree Hari Sureshbabu, Sabre Kais

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs-Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

Daniel J. Taylor

Ellen B. Stechel

Florian Goth

Abstract The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.