Quantum variants of machine learning algorithms are discussed with emphasis on methodology, learning techniques and applications in broad and distinct domains of chemical physics.

We introduce and analytically illustrate that hitherto unexplored imaginary components of out-of-time order correlators can provide unprecedented insight into the information scrambling capacity of a graph neural network. Furthermore, we demonstrate that it can be related to conventional measures of correlation like quantum mutual information and rigorously establish the inherent mathematical bounds (both upper and lower bound) jointly shared by such seemingly disparate quantities. To consolidate the geometrical ramifications of such bounds during the dynamical evolution of training we thereafter construct an emergent convex space. This newly designed space offers much surprising information including the saturation of lower bound by the trained network even for physical systems of large sizes, transference, and quantitative mirroring of spin correlation from the simulated physical system across phase boundaries as desirable features within the latent subunits of the network (even though the latent units are directly oblivious to the simulated physical system) and the ability of the network to distinguish exotic spin connectivity (volume law vs area law). Such an analysis demystifies the training of quantum machine learning models by unraveling how quantum information is scrambled through such a network introducing correlation surreptitiously among its constituent subsystems and open a window into the underlying physical mechanism behind the emulative ability of the model.

In this work, we study the magnetic phases of a spatially modulated chain of spin-1 Rydberg excitons. Using the Density Matrix Renormalization Group (DMRG) technique, we study various magnetic and topologically nontrivial phases using both single-particle properties, such as local magnetization and quantum entropy, and many-body ones, such as pair-wise Néel and long-range string correlations. In particular, we investigate the emergence and robustness of the Haldane phase, a topological phase of anti-ferromagnetic spin-1 chains. Furthermore, we devise a hybrid quantum algorithm employing restricted Boltzmann machine to simulate the ground state of such a system that shows very good agreement with the results of exact diagonalization and DMRG.

We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz $A(\overrightarrow{\alpha })$ from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy, thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ Hamiltonian using rotation and reflection symmetry and $H_2$ Hamiltonian within $S_z=0$ subspace using $S^2$ symmetry. We have found the variationally trained unitary gives good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers.

Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing $Tr({\rho }^2)$. The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows.